What you see is what you mean!
Lyx is an extremely powerful document processor, which allows you to create professional looking documents quickly, easily, with no worries about the style and layout.
LyX is a graphical interface WYSIWYM (What You See Is What You Mean) document processor to the LaTeX word processing package that encourages an approach to writing based on the structure of your documents, not their appearance. LATEX is a typesetting system which is very popular with computer scientists, engineers, mathematicians, physicists etc.
Of course, deriving from TeX and LaTeX, it will be no surprise that LyX excels at typsetting mathematical equations. In fact, LyX includes a very nice GUI equation editor, which permits the most common mathematical typesetting jobs to be done without having to resort to TeX control sequences. But LyX has, also, a native table creation facility based on the TeX/LaTeX model and advanced features for labels, references, index and bibliography.
Lyx is intended for people who write and want their writing to look great without tinkering with formatting details, font attributes, or page boundaries. Then, for writing with LaTeX, you may use LyX because it hides the ugliness of LaTeX source code.
On screen, it looks like any word processor (see slideshow below), but it uses the TeX engine for printed output and producing richly cross-referenced PDFs. The idea behind LyX is that the user selects a document class, such as Article, Report, Book, Letter, Slides or make the manual of your favorite program (e.g. NGSPice's manual was made using LyX), and LyX provides the structure.