This article is from the X-Men Comic Books FAQ, by Kate the Short (firstname.lastname@example.org) with numerous contributions by others.
The two Psylockes are an unusual matter. After the fun with the Siege
Perilous, Betsy Braddock was caught by the Hand, a bunch of techno-
demonic ninjas, and apparently turned into an Asian woman (UXM #256),
for reasons too vague to go into here. While odd, and apparently mainly
an excuse to draw Betsy in a bunch of tight-fitting quasi-Asian outfits,
it was still accepted that Psylocke was Psylocke. She just looked...
Then Revanche entered the scene (X-Men #20). She looked just like
Betsy's old body, but had an Asian name (Kwannon). Confused yet? In
another retcon, the unconscious Betsy apparently was discovered by the
original Kwannon after tumbling out of the Siege. Kwannon, who looked
just like the new Betsy's Asian form, touched her and got psychically
zapped by Betsy, somehow passing both Betsy's powers and personalities
to Kwannon, while passing Kwannon's personality to Betsy.
Enter the Hand. The head of the Hand, Matsuo Tsurayaba, was in love with
Kwannon despite her belonging to a rival ninja clan. Now, apparently the
original Betsy was not turned into an Asian, but the Asian body of
Kwannon was brainwashed by the Hand into believing that she was Betsy.
In this they had help from the demonic dancer of Mojo, Spiral. Meanwhile
the original Betsy's body was programmed by Spiral, behind the scenes,
to still think it was Betsy but remember that it was Kwannon once, just
to bug Matsuo. All of this was sorted out in X-Men #31-32.