In music, creativity is the ability balance newness with repetition. To introduce new ideas and frame them in terms of old ones, or reconnect old ideas in a new way. To give a very simple example, sing Yankee Doodle.

You'll notice that the beginning of the first two lines "Yankee doodle" and "Riding on a" are exactly the same notes, but they finish differently, a new listener can understand the the second line in terms of the first, but his expectation of how the second line will end is broken.

The is a very simple example, but balancing a listener's expectations, while having enough repetition or consistency* across multiple instrument lines and across larger sections of the music, so that there is global structure in addition to local structure is what makes real music. Komponisto has much more to say on this, but its scattered throughout many comments. I took me 2 years of bashing my head against traditional music theory, his preferred music theory, and composition classes to understand this, but I've become much more aware of what's going on inside a musical work.

I think that creativity is more generally the same thing, the ability to understand new ideas in terms of old ones or to reconnect old ideas in an interesting way. The question of how creative someone is, has to do with whether it feels natural for them to do this. Do they have to manually try out connecting ideas one by one, or does their brain seem to do it automatically? They can't help but try to find links and analogies in everything. And more interesting, can "brute force" creativity ever lead to creativity on auto-pilot? Extensions to physics are obvious (special relativity giving rise to general relativity) and fiction (narrative tropes).

*Stylistic consistency is more broad, it doesn't have to include the exact notes, it can include just the rhythm, or for example playing lots of leaps would be a type of style.