File extensions related to LaTeX, etc

.fd = Font definition; used in generating the output.

.bst = BibTeX Style File (e.g., a certain journal's preferred Bibliography layout settings); used by BibTeX when generating the bibliography.

.aux = LaTeX auxiliary file; created when LaTeX is run, these contain information LaTeX records which is then used by either BibTeX or LaTeX itself on later runs (e.g., about cross-references), and can contain other things as well. This file is created by running LaTeX but also used the next time LaTeX is run. It can be deleted, but then you may need to run multiple times in the future to regenerate it.

.bbl = Bibliography; this is what is outputted by BibTeX for insertion into LaTeX the next time LaTeX is run.

.blg = Bibliography (BibTeX) log -- just like .log but for BibTeX; generated by BibTeX and can be safely deleted if there's no need to check it for errors.

.brf = BackReference file for the backref package, I think. I'm not very familiar with these, but I suspect they're created by LaTeX when a file using that package is compiled.

.cls = Documentclass (like article, or report - if you have them cluttering up your folders, you must use a lot of custom classes for individual journals or universities, etc.) This is obviously used to generate the output.

.dtx = Documented source file; can be used to generate a LaTeX package or other file along with its associated documentation.

Of these, .aux and .blg can be safely deleted. Probably .bbl too if you don't mind rerunning BibTeX and have access to the .bib files needed. The rest should not be deleted but maybe moved somewhere more appropriate. In particular .fd, .cls, and .dtx are better taking up space on a (personal) TeX tree, not in the folder of the document you're working on.

General

Manually created

• .tex: The document itself
  Created by you.

Automatically created

• .aux: An auxiliary file that saves information for the creation of ToC, references, indices, bibliographies and other things like that. It is reread in the next compiling to create the ToC, references etc.
  Created by (pdf/xe/lua)(la)tex

• .toc: An auxiliary file that stores the Table of Contents, read in on subsequent runs to create the actual ToC.
  Created by (pdf)latex, xe(la)tex.

• .lof: An auxiliary file that stores the List of Figures, read in on subsequent runs to create the actual LoF.
  Created by (pdf)latex, xe(la)tex.

• .lot: An auxiliary file that stores the List of Tables, read in on subsequent runs to create the actual LoT.
  Created by (pdf)latex, xe(la)tex.

• .log: Stors all messages of the compilation, like errors and warnings. It’s used by most Editors / LaTeX IDEs to show the errors in you document.
  Created by (pdf)latex, xe(la)tex.

• .pdf: The common output format for your document.
  Created by pdflatex, xelatex, ps2pdf, dvipdf.

Bibliographies

Manually created

• .bib: The data base file containing your bibliography entries.
  Created by you.
• .bst: BibTeX style file.
  Determines how the bibliography looks (usually downloaded from somewhere).
• .bbx: A biblatex bibliography style.
  Created by users.
• .cbx: A biblatex cite style.
  Created by users.

Automatically created

• .bbl: bibliography environment, generated by BibTeX.
  This is what the call to bibtex produces and what is included into your document by the \bibliography command.
• .blg: bibtex and biber log file.
  Created by bibtex/biber.
• .bcf: biblatex control file.
• .run.xml: biber XML file.
• -blx.bib: biblatex control file.