Or you could actually just read the source code of the libs you are using...
It's pretty easy to miss a terminating semicolon which will waste time, but the real use case is for people who are writing the libs that other people are using; they have absolutely no knowledge or control of what other javascript might be prependend or appended onto theirs.
If 3rd party A omits a trailing semicolon, or 3rd party B doesn't uses your semicolon prefix style then by wrapping your script in semicolons you pre-emptively prevent problems.
I believe this is an example of the wider coding style called "defensive coding".