Extensions
SQLite includes a number of extensions providing additional functionality. All extensions are disabled by default and you need to take steps to have them available at compilation time, to enable them and then to use them.
If you get APSW from PyPI or are using SQLite from your Linux/BSD platform then they all enabled usually.
FTS5
FTS5 is the full text search extension. APSW includes comprehensive functionality..
ICU
The ICU extension provides an International Components for Unicode interface, in particular enabling you do sorting and regular expressions in a locale aware way. The documentation shows how to use it.
RTree
The RTree extension provides a spatial table - see the documentation. There are no additional APIs and the documented SQL works as is.