LaTeX is a set of TeX macros created by Leslie Lamport.
LyX is a document processor rather than a word processor. It relies on the typesetting features of LaTeX. Using LyX you concentrate on the content and trust LaTeX to look after the presentation.
LaTeX provides the following document processing benefits which are not available in word processors:
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Consistent sizing and spacing and layout of headers for chapters, sections, subsections, etc.
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Appropriate kerning of characters (squeezing or spreading of adjacent fat and thin letters)
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Ligatures (special glyphs) for letter combinations such as ff, fl, fi, etc.
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Automatic elimination of widows and orphans
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Treating pages and paragraphs (rather than lines) as units for typesetting
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Correct pagination: Odd pages on the right, Chapters starting on odd pages, etc.