What contributed the most to human migration more than ten thousand years ago?

Sturdy boats were invented.

Another Ice Age occurred.

A major volcano erupted in Africa.

A severe drought occurred.

I would say that the likely candidates are the first and the second option, the rest is not as likely to contribute to human migration.

Now, as far as I know, most Island-hopping happened actually in more primitive boats. Ice Age (that's my choice) allowed people to reach a whole new continent - America, by lowering sea level and freezing over Berin Strait - so I think this had the biggest influence!