She is not human.
From "Time's Arrow", we know that Guinan lived in San Francisco prior to 1889, which makes her roughly 500 years old at the time of TNG (in fact, somewhat older).
In San Francisco, she led the life of a wealthy, privileged upper-class person. She is very obviously afro-american -- not of the slightly-café-au-lait type, but pitch black -- and yet she is accepted and well-respected as a member of high society years before black rights were established. Even a prominent writer of that time who served as confederate partisan and prevalently used the N-word in several of his books very highly respects her (... mind control?).
Guinan mentions ("Q Who") that she was not around at the time the Borg destroyed her home world a century ago and left virtually none alive, but she was told (by whom?!) about it. This might suggest she stayed on Earth for another few centuries.
Nevertheless she was aboard the SS Lakul. Which happened, roughly, a century before "Q Who", and happened to be on its way in the opposite direction.
The fact that she is too old to be human, the fact that she "listens" (and insists on saying: "I listen.") and that she was on an El Aurian refugee ship suggests that she is El Aurian.
She is not El Aurian
"Generations" places her on the Lakul together with Soran, fleeing from her home world after it has been destroyed by the Borg. Which, as we know, happened when she was not around. That would however mean she needed to be in two locations at the same time.
Further, she is at least 300 years older than a clearly aging El Aurian who is said to be "almost 200 years old", without showing any signs of age herself.
El Aurians are "ordinary" living beings by all measures. They may "listen", but they have no other special powers. In particular, they are no challenge to Q.
However, Guinan is able to sense discontinuities in the time continuum, she is able to see into parallel universes, she can sense the presence of Q, and most importantly, she seems to be equal in power to Q.
Q seems afraid of Guinan, and she seems confident being able to fight Q with some three-finger hand gesture. Guinan talks of Q and the Q as if they were old acquaintances or as if she was one of them, and Q tells Picard that she is not what she appears to be (he calls her an evil spirit that attracts mayhem wherever it goes).
She is not El Aurian with Nexus super powers
Guinan was in the Nexus aboard the SS Lakul and torn away from there when the survivors were saved, just before the ship exploded. Arguably "something of her" stayed in the Nexus.
Since inside the Nexus you exist at any and all time you desire, it seems plausible that this "echo" of yours that is left back when you leave the Nexus provides some particular sensitivity for time.
However, while residual Nexus super powers might explain for this sensitivity, they do not lend for powers that rival those of Q. Also, no other El Aurian from aboard the Lakul, including Soran, is mentioned having any "special powers" (other than being empathic listeners and good con men). Picard doesn't have special powers either although he was in the Nexus.
Residual Nexus super powers also do not explain how she could have gotten to Earth in finite time centuries before the simplest warp drives were known if the Enterprise needs close to 3 years at maximum warp speed ("Q Who") to get to the sector where her people is from. If the El Aurians were so advanced 500 years earier already, they would be technicians in the TNG setting, not con men.
Except of course, if Guinan had used the Nexus to travel from the Lakul to 1889 San Francisco, then she might indeed have made the trip. That is, however, not compatible with the established timeline (she demonstrably didn't do it, as she was rescued from the Lakul).
She is not Q
We never see her use Q powers. The most advanced special power that we see her use is unerringly telling Picard that something is wrong (which may extend into a different time line or universe).
This is admittedly a Q power (seeing how Q being told not to act as if he knew everything replies: "But I do know everything."), but it seems untypical.
Also, the Borg would surely not be able to assimilate a Q or destroy the Q home world, if they had a home world.
So... just what is she?
