What?
A .diff file is a file generated by GNU diff, taking two sets of files and generating a patch describing the differences between the two sets. This patch can be used by GNU patch to patch an old file set to a new one, without having to manually edit files.
Why?
By using a patch, users should not edit any files manually or overwrite complete files, eventually losing changes made to the source code.
How?
The diff file can be downloaded from the download section. To use it, you need a version of GNU patch (generally available on Linux) or a Windows port of it. To apply the patch, you place the diff file in your forum's directory and execute:
patch -p1 < usebb-<version>.diff
replacing <version> with the current version.
If successful, you forum will be updated to the latest version. If not, you will have to alter the files manually (probably because changing lines were not original anymore).
A list of changed files can as well be downloaded from the download page.

Thanks for this!