TeX is both a program (which does the typesetting, tex-core) and format (a set of macros that the engine uses, plain-tex). Looked at in either way, TeX gives you the basics only. If you read the source for The TeXBook, you'll see that Knuth wrote more macros to be able to typeset the book, and made a format for that.
LaTeX is a generalised set of macros to let you do many things. Most people don't want to have to program TeX, especially to set up things like sections, title pages, bibliographies and so on. LaTeX provides all of that: these are the 'macros' that it is made up of.
First, Mike's answer is quite good. I will mostly expand on it and provide more details.
TeX
TeX is a language (a full programming language, actually) for typesetting documents. It originally output to a format called DVI which could then be converted to PostScript, PDF, etc.; more recent versions can output directly to PDF. You write a document with TeX instructions in it, and the TeX system will convert it into printable material.
TeX is used for a wide variety of documents, particularly in science and academia. Most people use it for things that other people would likely use Word for; however, the quality of its results are more on a par with InDesign or other major document layout packages, far superior what word processors generally yield. Designing specialized or ad-hoc document formats such as brochures, however, is probably easier with InDesign or QuarkXPress (although it is not impossible to do so in TeX/LaTeX).
TeX itself is quite low-level.
LaTeX
LaTeX is a macro package written in and for TeX that provides commands and defaults for writing larger documents at a higher level, taking care of things like sectioning, tables of contents, etc. In my experience, most TeX users do not write low-level TeX directly, but rather use LaTeX. LaTeX is not the only such package, though; ConTeXt is another macro package with a different design philosophy, but it sits at a similar level to LaTeX.
Usage
TeX and LaTeX are very widespread in some portions of academia, such as mathematics and computer science, due to its superb support for mathematical formulas. I have also heard that it is popular in some other disciplines as well, such as linguistics.
Best Answer
LaTeX makes it possible to do so much and so much that the simplest thing is to give examples of achievements:
tikzorpstrickspackages, see by example http://www.texample.net/tikz/examples/tag/3d/beamer classsee https://www.overleaf.com/gallery/tagged/presentation ;animatepackage; see http://texample.net/tikz/examples/tag/animations/asymptotethat can be manipulated with the mouse, see by example http://asymptote.sourceforge.net/gallery/truncatedIcosahedron.pdf to open with adobe reader to be able to manipulate the 3D object with the mouse;media9package see http://www.overleaf.com/latex/examples/using-media9-to-include-videos-files/yvdwwvpknjkk ;OCGlayer (package ocgtools, ocg-p, ocgx, ocgx2) see: http://mirror.hmc.edu/ctan/macros/latex/contrib/ocgtools/examples/ocgtools-example-web.pdf http://mirrors.ctan.org/macros/latex/contrib/ocgx/demo-ocgx.pdf open with adobe reader or a pdf reader that manages the ocg layers.fancytooltipspackage see http://mirrors.ctan.org/macros/latex/contrib/fancytooltips/examples/fancy-preview-demo.pdf open with adobe reader or a pdf reader that manages the ocg layers.pdfcommentpackage see http://mirrors.ctan.org/macros/latex/contrib/pdfcomment/doc/example.pdfhyperreforeformspackage https://martin-thoma.com/creating-pdf-forms-with-latex/