THE SERIES
The X-Files? FBI agents Mulder and Scully investigate paranormal phenomena of an episodic nature. That's pretty much it, besides the plot arcs, which range from interesting to brain-bleedingly BAD, but usually have Krycek in there somewhere and, so, are worth watching. *nod*
You don't need to know about the series to interact with Alex though. This is mostly just some information for those who want to know why I'm playing him so badly are curious as to where he's coming from and what I'm doing with him.
THE HISTORY
Alex Krycek came in as Mulder's new partner when the government disbanded the X-Files (for the first among many many times) and succeeded in getting into Mulder's pants earning Mulder's regard much more easily than Scully ever did, mostly because Krycek wasn't above ass-kissing and back-patting.
To not go too deeply into the plot (which is nine six seasons worth of brain-bleeding weirdness), Krycek ends up being a double-agent, working for the mysterious Cigarette Smoking Man (and organization he works with - The Consortium) who constantly plagues Mulder and Scully as a lynch-pin in the many conspiracies that they attempt to uncover and investigate during the series run.
At that point, things go downhill pretty swiftly, for Krycek in particular. His boss tries to blow him up to wipe out evidence he stole on their behalf, he becomes a freelance agent to sell the secrets he stole in his escape, he gets possessed by the Black Oil aliens, left in a locked silo for god knows how long, beat up by Mulder (and Skinner and eventually Doggett, I think), imprisoned in Tunguska, exposed as a Russian/KGB agent, he has his left arm sawed off by well-meaning Tunguska escapees hoping to keep him from being experimented on, imprisoned in Tunisia, then he returns to being a minion of the Consortium and, finally, gets shot in the head in the most confusing and ignominous end I've ever seen. Seriously, I still have no idea what he was doing that entire episode.
THE CHARACTER
Krycek's supposed to be a villain, though nearly nothing is certain in the X-Files universe. He switches sides whenever it's convenient and pisses everyone off at some point during the series. He's definitely not a nice guy, though I don't think he's evil either. Definitely of questionable morals and integrity and sexuality.
The only thing that is vaguely consistant is that he has his own motives and he'll follow those more than anything else. You're never told exactly what they are, but they seem to be some sort of ambition, a lust for power and prestige, and no particular loyalty to anyone unless it suits him.
As everything in the X-Files, Krycek seems fixated on Mulder, coming him on several occasions to be mysterious, annoying, smug and sometimes actually helpful.
THE REBIRTH
This Krycek died at the end of season 8 while attempting to kill Mulder for reasons that don't make much sense anyway.
Instead of going wherever it is dead people go, he woke up at Fandom High, full of memories of his past indiscretions life, but with a teenaged body. And two arms! He's pretty happy about that.
So far, he's not sure why he's here or how it happened. He's not the first person to come back from the dead (see: Mulder, gigantic stupid plot twist of DOOM), so it's not unprecedented, but it still leaves him with no answers and far too many suspects. Is it the Consortium? The Oiliens? The KGB? Who would want him as a teenager again?
His memories don't seem quite integrated with the whole, but that might be stress, it might just be his own way of dealing with everything that's happened. Right now he's keeping an eye out for anything suspicious while simultaneously trying to get himself some sort of influence in the school hierarchy. Being an intern seemed the best way to do that without getting involved in yet another group or conspiracy - he's had enough of those for the moment.