LyX is a fully featured document processor. Here are some of the features, classified by category.

Math/science features (demo clip)

  • Mathematical formula editor which is easily best of breed. Fully harnesses the power of LaTeX.
  • Equations can be entered via point-and-click interface or via keyboard with LaTeX commands (optionally via auto-completion). Formulas are immediately visually rendered on screen.
  • Copy/paste to and from LaTeX source code.
  • Equation arrays, equation numbering, theorems, customizable math macros, matrices, algorithms, and much more.
  • Support of math macros
  • Basic support for various Computer Algebra Systems (CAS) - Maple, Maxima, Octave, Mathematica

Structured document creation

  • Advanced features for labels, references, index and bibliography (including advanced BibTeX support)
  • Standard word processor operations, like cut/paste, multiple open documents, undo/redo, spellchecking (uses aspell or hunspell in the background), thesaurus and revision tracking
  • Different textclasses allow you to type letters, articles, books, movie scripts, LinuxDoc, slides, presentations. Also included are some textclasses for scientific societies, such as AMS, APS, IEEE, or specific journals like Astronomy and Astrophysics.
  • Dedicated modules let you dynamically enhance the functionality of the textclass by adding features that are needed for specific tasks (such as endnotes, linguistic glosses, Noweb/Sweave or LilyPond support)
  • Numbered section headings, table of contents (with hypertext functionality), lists of figures/tables
  • The outliner mode allows for easy navigating in your document as well as for moving or nesting complete chapters and sections
  • Character styles provide access to fully semantic markup

Graphics/tables

  • Support for many graphic formats (including EPS, SVG, XFig, Dia and others)
  • WYSIWYG for cropping, rotation, scaling of images
  • Enhanced support for intelligently floating figures and tables
  • Support for subfigures, subtables and captions
  • Support for wrapped figures and tables
  • Interactive WYSIWYG tables
  • Shared (geometry) settings for multiple figures

Internationalization (more here)

  • Support for writing documents in many languages of the world
  • Bidi support for Right-to-Left languages such as Hebrew and Arabic
  • Support for many writing systems (including CJK)
  • Write multilingual documents consisting of diverse languages and scripts thanks to unicode compliance.
  • Menus, error messages, manuals and key bindings are available in many languages

Document formats

  • Access to all LaTeX functionality with capability to insert plain LaTeX code anywhere in a document.
  • Import and export to many formats (LaTeX, PDF, Postscript, DVI, ASCII, HTML, OpenDocument, RTF, MS Word, and others) thanks to configurable converters
  • Send a fax from within LyX
  • Source code viewer for instant LaTeX and DocBook view.
  • SGML-tools support (DocBook DTDs)
  • Literate programming support (noweb, Sweave)
  • Support for export of PDF bookmarks and header information

Usability/user interface

  • Graphical user interface that gives access to all functions via menus and mouse, as well as configurable key bindings
  • Extensive documentation, including a beginner's tutorial, available in many languages
  • Text completion support
  • Typesetting in background

Document management

  • Change tracking
  • Support for external version control systems (RCS, CVS, SVN, Git)
  • Comparison of different versions of the document
  • Branches for having different versions of the same document
  • Yellow sticky notes

Additional

  • Available for Linux, Windows, and Mac
  • Quite fast and no memory hog at all.

There's a lot more not listed here. Check it out yourself!