This is ultimately a very deep question. We do not have a very easy ability to answer it at this time. Let me give you the pieces that we presently have.
The basic interactions.
The world as we know it today consists of five fundamental things that happen; they are all called "fields" and the first four are called "forces" or "interactions". In rough order from strongest to weakest, these 4 are as follows.
- Protons and neutrons are sticky and stick together into atomic nuclei. This is called the strong nuclear force or the strong interaction. Some matter does not feel the strong force; these particles are called "leptons." Some matter does, and they are called "quarks" (and combinations of them are called "hadrons").
- Radioactivity. Neutrons want to turn into a proton-plus-electron-plus-antineutrino triad. In particle physics this is known as the weak nuclear force, or the weak interaction.
- Chemistry. Protons attract electrons and repel protons; electrons repel each other too; they emit light under certain conditions. To particle physics, this is all known as "electromagnetism."
- Things fall down. Matter mysteriously attracts other matter through an unscreenable infinite-range force known as "gravity".
In those four interactions, and mostly in that third one, we think we can find mostly everything that happens in this world. The fifth interaction which is conspicuously absent is the "Higgs field", which we'll talk about in a moment.
We cannot give you a great explanation why Nature hasn't chosen fewer interactions or more interactions; in particular we cannot tell you a deep reason why Nature chose for there to be an electromagnetic interaction at all. We can give you details but you can always persist asking "why" until we find ourselves in ignorance.
And then there was unity.
We can tell you some other things about electric charge though. A full classical theory was available per James Clerk Maxwell, and a full quantum theory became available due to the works of Schwinger, Tomonaga, and Feynman. This became a template for understanding the strong force, with photons replaced by "gluons" and electric charge replaced with three "color charges" (called arbitrarily "red", "green", and "blue") which has to balance out either in the same way that electric charge does (quarks plus antiquarks) or else by having even amounts of the three charges.
In particular, physicists beat their heads against a wall trying to describe the weak interaction in a way that (a) didn't have unphysical consequences and (b) played nice with quantum relativity until 1961, when a young Ph.D. named Sheldon Glashow discovered that you could make relativistic quantum theory and the weak interaction play nice together if you "bundle in" the electromagnetic force and describe them both together, mediated by four types of 'virtual' particles: two of those particles, the Z boson of the weak interaction and the photon of electromagnetism, at very high energies can phase into each other.
Glashow's "electroweak" theory had some unphysical consequences at high energies, which were removed in the mid 60s by postulating this fifth fundamental interaction, which everyone calls the Higgs field. The Higgs field has a weak coupling to all of the "matter" particles but also to some of the "force" particles, giving them mass. In short, the Higgs explains why everything which is not a proton or a neutron doesn't zip off at the speed of light. We believe these days that we've definitively observed some statistical effects of the distinctive particle which quantizes the Higgs field, shedding most of our doubt about this explanation. The interaction-energy that these particles have due to interacting with the Higgs field grants them an effective mass via $E = mc^2$.
Does this habit of Nature unifying these forces go further? Maybe. So-called "grand unified theories" unify the electroweak interaction with the strong interaction, but they often have some strange predictions, like magnetic monopoles or that protons will eventually decay into positrons-plus-photons, which we've never actually seen happen. So it's very hard to endorse these theories at this stage. So-called "theories of everything" incorporate gravity as well.
However, here we're at a significant experimental loss: we simply don't have enough experimental confirmation to decisively say "yes, this grand-unified-theory is good; no, that theory is bad."
What the electroweak theory tells us about charge.
Okay, now that you know that the electromagnetic force is a low-temperature part of this electroweak theory, what does that tell us about electric charge? It says that electric charge comes about as part of two conserved quantities, called "weak isospin" or $T_3$ and "weak hypercharge" or $Y_W.$ The quarks, for some reason, have a weak hypercharge of +1/3. The leptons, for some reason, have weak hypercharge -1. Some things, in addition, have weak isospin +1/2, and some things have weak isospin -1/2, in the same units. What are those reasons? I don't think we really know. (Also don't get too attached to the pluses and minuses; there are 4 "antiparticles" for each of these particles that have the opposite sign for all of them.)
Electric charge in these units is $q(T_3, Y_W) = T_3 + \frac{Y_W}{2}$, leading to four classes of particles: the non-electromagnetic non-strong neutrinos $q(+ \frac 12, -1) = 0$, the electromagnetic non-strong electrons $q(-\frac 12, -1) = -1$, and the electromagnetic strong quarks "up" $q(+\frac 12, +\frac 13) = \frac 23$ and "down" $q(-\frac 12, +\frac 13) = -\frac 13.$
So for example a neutron is made of two downs and an up, total charge $2\cdot\frac{-1}{3} + \frac 23 = 0.$ The weak force will sometimes turn one of those downs into an up plus a $W^-$ boson $q(-1, 0) = -1$ , which then turns into an electron $q(-\frac 12, -1) = -1$ plus an electron antineutrino $q(-\frac 12, +1) = 0.$ The two ups and a down quark will then make up a proton $\frac{-1}{3} + 2\cdot\frac 23 = +1.$
Particles, in short, are charged because they have this intrinsic weak-isospin and this intrinsic weak-hypercharge which they cannot shed. We do not know why they have these exact parameters, except that all of the possibilities are fully represented.
Mass discrepancies.
We've secretly also answered why protons and neutrons have a mass so much higher than the electron: the electron is a single particle which does not feel the strong force; the protons and neutrons are made up of three quarks which are bound together by the strong force. (In general that is a property of the strong force: it is caused by a powerful three-way charge that we call a "color charge"; the color charge has to balance out either by having three particles which each have one the colors, or by having a particle and an antiparticle bound together with the same color charge; if it's not balanced out it will tear particles made with the other weaker forces apart until it is satisfied because it is so strong.) Satisfying the associated strong force comes with a binding energy $E$ which acts like a mass via $E = mc^2.$
Neutrinos and electrons, which don't feel this energy, only get a little bit of mass from their comparatively weak couplings to the Higgs field: up and down quarks also have a little mass from this mechanism. This is much smaller than the binding energy however; it is maybe 1% if the proton/neutron's mass, most of which comes from this strong force.
So that's the tip of the gory details that go into particle-physics. I don't think we can tell you yet why those particular weak hypercharges are associated with having color charge (feeling the strong force) or not; we wouldn't know until we could reliably test the correctness of grand-unified theories and determine which one our electroweak interaction is embedded in, if there even is one. (Nature might just say, "no, that's just the way I roll, no further questions.") In some GUTs, weak hypercharge is totally separate from color charge; in others part of weak hypercharge unifies with color charge at high-enough-energies.
Best Answer
It depends on the context or to what extent. In metal, outermost electrons are ionized and form electron sea. The metal contains metal cations and free electrons. When applying a voltage on the metal, electrons move and form electric current. If some electrons are removed or added on the metal so that there's net charge on the metal, electrostatic field is produced.
On the other hand, when a photon has sufficient energy (i.e. the wave frequency is high enough to overcome the work function) hitting on the metal surface, electrons may leave the metal, this is called the photoelectric effect. In this case, the photoelectric current can be regarded as a stream of free electrons.