Warning: Season Five spoilers do appear below.
Season One of ANGEL found the show trying to establish itself, its moods, its major characters, its bad guys, and its story arcs. For a first season, it was not at all a bad show; it was, in fact, quite good. But it didn't truly match the high standards set by BUFFY THE VAMPIRE SLAYER. In Season Two, however, Angel Investigations truly came into its own. It moved from a spin off finding its own rhythm, to a truly superb show in its own right.
Season Two is somewhat unusual in that it actually features two major plot lines. First, there is the stunning revelation that Wolfram and Hart has managed to resurrect, in fully human form, Angel's old love and sire Darla. Her return, use, and abuse by Wolfram and Hart constitutes most of the season's episodes. She is not the only character we first met in Buffy to guest on the second season: Harmony, one of the original Cordettes, comes to LA to visit Cordy. The visit generates perhaps the funniest scene in the entire series, when Harmony, who unbeknownst to Cordelia is now a vampire, is barely able to resist feeding off her in her sleep. When Cordelia wakes up just in time, she wrongly thinks that Harmony was now gay. The ensuing conversation of errors is hysterical. As we approach Season Five, it has been disclosed that Harmony will be back in LA in Season Five, somehow or other working as Angel's secretary as he takes over as director of Wolfram and Hart. With Cordelia no longer a part of the show (in my opinion, the dumbest decision in the history of the show; Joss Whedon claims in interviews there is nothing more to do with her character on the show, but I think that is palpable hogwash), Harmony has the potential of bring a bit of whimsy to the show.
The Darla story line is a dark one, with tragic circumstances thwarting Angel's attempts to lead Darla to the path of righteousness, and seems to succeed, even when Darla learns that she is doomed to die as a mortal. His involvement with Darla leads to Angel breaking off his involvement with Cordelia, Wesley, and Gunn. Much of the interpersonal dynamics of the entire season revolve around Angel's alienation from his friends, and his gradual restoration of their friendship.
The other major plot line of the second season involves first Cordelia and then the others traveling to the dimension of Pylea. Now, I liked these episodes myself, but there is little question that for a huge number of fans, these are among the least popular episodes in the history of the Buffyverse. For the series as a whole, the most important thing to come out of this arc is the rescue of Fred, a brilliant physics student who had been accidentally trapped there. Despite Cordy, the show had until them had an overwhelmingly male feel to it. In season three, as Fred becomes an integral part of Angel Investigations, she brings a crucial element to the show's chemistry.
Two other major developments take place in Season Two. First, the introduction of the character of The Host aka Lorne, a demon from another dimension (actually, Pylea, we later learn) who can read anyone's aura when they sing. Hence, he is the owner of a karaoke bar. Lorne would later be elevated from supporting character to a permanent character. The other major change, and one crucial to the ambiance of the series, was Angel Investigation's moving into an abandoned hotel. I liked this setting so much that I am going to miss it tremendously as we move into Season Five.
All in all, Season Two represents a major achievement by a team that seems to be incapable of producing a less than remarkable product. And, of course, the set is essential for any lover of things Buffy/Angel.