What is XeLaTeX?
Strictly speaking, XeLaTeX is a format and XeTeX is the underlying TeX engine; see The levels of TeX for more information.
Leaving technical details aside, we can briefly summarize the situation as follows.
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LaTeX produces output in DVI format. Accented letters and other diacritics have to either be entered using arcane commands such as
\'e
for “é”, or saved in a given encoding and correctly declared using the package inputenc. -
pdfLaTeX is a development of LaTeX that generates output in PDF directly. It has been the default engine in TeX distributions and editors since about 2010, so you have been using it whether you know it or not. Encoding issues remain the same as with standard LaTeX.
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XeLaTeX is a modern engine originally developed to load fonts of the operating system directly. Essentially, XeLaTeX produces PDF output. It overcomes encoding issues by using only Unicode (UTF-8) encoded text as input. One of the main advantages of XeLaTeX is the support for modern OpenType fonts.
If you write in a language other than English and want to try fonts other than Computer Modern in your LaTeX documents, you should probably switch to XeLaTeX as your default engine. It is mostly a matter of configuring your editor accordingly.