I'm not very surprised that a lot of answers relate to the mechanical aptitude of learning and playing an instrument.
Now is this talent ? Or is this a matter of excercise ? I agree that (like Rharv said) some learn faster then others, so talent would be related to the speed that you learn something ?
Now how about this : I saw an interview of Marc Knopfler, and the interviewer said to Marc that he was impressed with the 'talent' he had... on which Marc replied 'talent ? no, this has nothing to do with talent, i'm practising every day between 6 and 8 hours....'
I do agree that there is a notion of talent, somewhere, but i think it has a very unimportant factor. Of course in this theory you have to count out the real exceptions, like the 4 years old prodigy and on the other side the people that have no rythmic feeling at all and can't count to 4...
With the experience i have now, I would say that it is much more a question of wanting to do something and perceferance. A known theory is that it takes around 1000 hours of practising to play an instrument and around 3000 hours to master it completly. And again i'm excluding extremes like professional classical or jazz players who practise there whole live to achieve a certain level.
But I would say it depends allso on the way how you learn it and how it is teached.
As an example, take bass. Beside hearting your fingers at the beginning
it is just a matter of learning patterns on the neck. And if that is teached in the right way, a student should be able, after a defined amount of time, to play allmost everything in a reasonable (acceptable) good way. I can't believe my ears when a bass player says, 'sorry i can't play in that key' ! and i'm not sure that is his fault or rather the teacher that told how to play bass.
But since bass is a lot about thinking in patterns, isn't it then more an aptitude of reconizing pattern (which is mathematical) then an aptitude of music ?
The definition of musical talent isn't that easy....