In addition to Werner's excellent answer I'd like to make some remarks.
The indent after a section title (section is used here in a very broad sense, that is, anything with a title) is a question both of personal taste and of typographic tradition.
Tschichold, for example, states that the first indent should be suppressed only after a centered title and that all other paragraphs must be indented (see notes). The Imprimerie Nationale, which the French consider as the supreme guide in typographical matters, states that the first indent must always appear. In British (and US) typography the first indent is usually suppressed. Other national typographic styles follow one or the other trend.
Some language modules for babel
change LaTeX's default of suppressing the first indent: Albanian, Chinese, French, Galician, Serbian, and (Castilian) Spanish. Polyglossia extends the list: Albanian, Asturian, Basque, Breton, Catalan, Croatian, French, Galician, Greek, Interlingua, Italian, Occitan, Serbian, and (Castilian) Spanish.
The most important criterion to follow is being consistent across a document. Nobody (except perhaps in France) will hold against you a typescript where the "national tradition" isn't followed. However, breaking a well established tradition mustn't be taken lightheartedly, but also not too seriously.
The Spanish module for Babel allows for changing the style (the others don't). For Polyglossia here's what I do when I write a document in Italian:
\usepackage{polyglossia}
\setmainlanguage{italian}
\PolyglossiaSetup{italian}{indentfirst=false}
(yes, I like suppressing the first indent, also after noncentered titles).
Best Answer
There are publications that indicate paragraphs by leaving some extra space between them (most often with ragged right typesetting) but I would claim that they are in the minority if you go into a library and open books at random, so I'm a bit surprised you state you have never encountered them in "real" life".
Perhaps your background is CJK scripts in which case the situation is probably different.
The most common approach in "western" typography (which is where TeX originate) is to typeset text justified and (last not least to save space) not to put extra white space between paragraphs. If you do this, then you have the issue that the last line of a paragraph can become completely filled once in a while. To be able to nevertheless always enable the reader to see that a new paragraph has started the first line therefore typically indented by a small amount (and since after a heading this visual clue is unnecessary it is normally left out). That's about the background.
But there is no reason to "struggle" with it. If you do prefer a different style, LaTeX actually makes it easy for you to adjust your documents to any style and there is no need to go
\noindent
on every paragraph as you might have feared from the description on overleaf (that just describes how to turn it off for individual paragraphs which is sometimes useful. Instead use a package such asparskip
or a class that sets up the style you prefer automatically.