Deja, "perfect pitch" is the ability to tell what a note is when played or (in more advanced form) to sing it when asked, without a reference note.
Most people with any musical training, if you play them say middle C on the piano and tell them what it is, and then play the G above it but don't tell them what it is, could name the G. They've learnt the sound of the interval between two notes five steps apart in the scale. This is called "relative pitch". It's how even non-musicians know how to sing a tune, or when a note in a tune they know is wrong.
The difference with the person with perfect pitch is that if they get up in the morning having heard no music that day, or even the past few days, and you don't give them any known reference note but just play the G out of the blue, they can tell you it's a G. It's a completely different kind of hearing and learning: they know the "chroma" or sound quality of each pitch as a thing in itself.
Actually perfect pitch is a misnomer. The better term is "absolute pitch" because this describes the difference between hearing a single note absolutely, and judging the connection between two notes relatively. I dislike the term perfect pitch because it leads people to think that it's one end of a continuum, which it isn't. In actual fact, the absolute pitch of people who have it is no more "perfect" than well trained relative pitch. People with absolute pitch still make errors, and they vary in their degree of tolerance of slightly out of tune notes before they no longer recognise them as the same note.
Unlike relative pitch, perfect pitch can't be learnt as an adult. There are various schools of thought about whether it is genetic, whether it emerges out of early musical training, or whether it can be taught but only in a "critical period" of early childhood. Actually I'm intrigued by your DD having it as one of the most agreed factors is that the vast majority of people with it had music lessons before the age of about 7, and I gather she didn't start till well after that.
It's sometimes said that it has various disadvantages like making it hard to transpose or sing in a choir that is slightly out from A440. I think these are overdone to be honest. I've know plenty of singers with absolute pitch who have no trouble at all "switching it off" or moving between absolute and relative strategies as required. I think the truth is just that you still need relative pitch training. Absolute pitch doesn't replace the deeper musical understanding that comes with relative pitch - and it's the lack of that understanding that hampers some musicians, not the presence of absolute pitch.
On the positive side, I've noticed it seems to massively increase the speed with which people can internalise and memorise music, which may have something to do with your DD's rapid progress. It's very useful for things like advanced score reading and anything requiring an instant connection between sound and symbol. The majority of famous conductors seem to have it, for example.