Jay wrote:Cordelia appears in the spin-off 'Angel' series, its first season ran at the same time as Buffy Season 4. Not sure how it's explained because I haven't actually seen Angel S1 since it first aired in 1999!
BUFFY GEEK ALERT! Here's a breakdown of what happens to Cordy. Hope I haven't put any spoilers.
After Cordelia's family end up broke at the end of Buffy Season 3, she goes to LA to become an actress as she can no longer afford college. There she meets Angel at a party where he's protecting a girl. In LA she's still broke, lives in a horrible apartment and steals food from the party to eat. After Angel saves her from a vampire, and she helps patch him up after he's shot with bullets. She then sets up Angel Investigations and offers to work there until she's rich and famous. She insists on charging people for helping them (which Angel is initially against) and comes up with the tagline "We help the helpless".
In the third episode of Angel, Oz travels to LA to give Angel the Gem of Amara and reunites with Cordelia. It's implied that he lets the gang know she's working with Angel when he returns to Sunnydale. In the Buffy episode 'Pangs', Angel returns to Sunnydale to protect Buffy in secret. When he encounters Willow, she asks "Is it true Cordelia works for you?"
Cordelia isn't often mentioned on Buffy after this, except when Buffy says Glory reminds her of Cordelia. In Season 2 of Angel, Harmony travels to LA and meets up with Cordelia who initially doesn't know she's a vampire. Cordelia is then seen calling Willow, who tells her Harmony is a vampire.
If you like Cordelia then I would strongly recommend watching Angel. Her character arc on Angel is a true highlight of the show (except for Season 4 which I mostly try to forget).