LaTeX is a system for typesetting documents. It was originally created by Leslie Lamport in 1984, but has been maintained by a group of volunteers for many years now (https://latex-project.org). It is widely used, particularly but not exclusively for mathematical and technical documents.
A LaTeX user writes an input file containing text to be typeset along with interspersed commands. The default encoding for the text is UTF-8 (as of 2018). The commands specify, for example, how the text should be formatted.
LaTeX is implemented as a set of so-called “macros” (a TeX format) which use Donald E. Knuth’s TeX typesetting program or one of its derivatives, collectively known as “engines”. Thus, the user produces output, typically PDF, by giving the input file to a TeX engine. The following sections describe all this in more detail.
The term LaTeX is also sometimes used to mean the language in which the input document is marked up, that is, to mean the set of commands available to a LaTeX user.
The name LaTeX is short for “Lamport TeX”. It is pronounced
LAH-teck or LAY-teck, or sometimes LAY-tecks. Inside a document,
produce the logo with \LaTeX. Where use of the logo is not
sensible, such as in plain text, write it as ‘LaTeX’.