LATEX is a macro package built on top of the typesetting package, TEX. TEX was written by Donald Knuth in the 1970s, and Leslie Lamport wrote LATEX as a higher-level, easier way to write TEX.
TEX was quite advanced for its day, and is still used (particularly by academics) because of its free availability and its flexibility in typesetting maths and other symbols. It's more like a programming language than a word processor, with embedded commands prefixed by a backslash and block structure. Like programs, TEX documents are processed by a `compiler', outputting a .dvi file, which is a device independent file which can be read by many converters for output onto physical devices, such as screens and printers.
A reason for its longevity is the ability to add facilities to TEX, using macro packages that define new commands.
LATEX is the most popular way to write TEX. Although WYSIWYG word processors and DTP packages are outstripping LATEX, the increasing interest in hypertext and mark-up languages makes LATEX relevant as a similar language to SGML documents (such as World Wide Web HTML files).
Also, languages such as LATEX (and Rich Text Format, which it resembles in many ways) are complementary to WYSIWYG packages. These languages allow automatic production and translation of documents, where manual mark-up is impractical or undesirable.
Since the source code of TEX and LATEX is in the public domain, there are many free and commercial implementations of LATEX for almost every computer in existance. Of PC implementations, EmTeX is arguably the best and most complete. You can download it from various FTP sites.
If you don't want to use LATEX itself, you may wish to use a program called lacheck to check your documents before using Tex2RTF, since it catches some mistakes that Tex2RTF doesn't.