What's the difference between include and require in puppet

They are very different things, actually. To say require B means B must come before A (and, therefore, can lead to circular dependencies if something in B turns out to require A). And if B is not included at all, it will lead to missing dependencies error.

On the other hand, include B just says B will be applied whenever A gets applied: it says nothing of the order between them.

This was just asked (and answered) on the puppet mailing list:

The difference is evident when the catalog needs to be applied. With include you have evaluated its contents at the time of the include - but any resources must be depended on explicitly after the include. With a require - the dependency is created for you - but you have to be careful and ensure that this is your desired result

- Ken Barber in Require vs Include?