But what if you do this:

    <script src='3rdpartyA.js'></script>
    <script src='yourscript.js'></script>
    <script src='3rdpartyB.js'></script>

You need the semicolon at both ends to insulate your script from the unknown coding style or 3rd party scripts which may be appended or prepended to yours.

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".