LaTeX is a typesetting system, most often used for technical or scientific documents.
Somewhat simplified, producing a document using LaTeX is a two-part process: you write the text without any formatting information (font size and type, page height etc) but add special codes describing what the text is; for example identifying headings, titles, formulae, etc. You then convert this into a document where all items of a particular type (for example all titles) look the same. This means that you do not have to worry about the appearance of the document while you write, but this is taken care of separately.
LaTeX is an open source product and you can download it for free. You can use a simple text editor (such as Notepad) to create your input files, but you may find that using a special editor makes the process simpler. A convenient comparison of different text editors is provided in Wikipedia (accessed January 2015): http://en.wikipedia.org/wiki/Comparison_of_TeX_editors.