While most life on Earth is being exterminated under a haze of mushroom clouds, the wheelchair bound Dr. Strangelove is miraculously healed. He leaps up from his chair, gives a Nazi salute, and famously cries, "Mein Fuhrer, I can walk!" (Apparently this line was improvised by Peter Sellers after he accidentally got up from the wheelchair.) It totally reminds us of some scene from a tent revival, where people are healed by an evangelizing faith healer. Only in this case, the person is an ex-Nazi weapons developer, and the healing comes via the idea of a post-apocalyptic age populated by racially superior ubermenschen and hot women. When it becomes clear that one of the bombers can't be recalled, Strangelove feels a kind of excitement thinking about a new world filled with a deliberately bred master race.

He can think about it, but ultimately he's vaporized with the rest of humanity. Remember that the events of the film are unfolding in parallel time; the people in the War Room don't know that the Doomsday Machine has already started to do its thing. Everybody's toast, superior or not. Strangelove's next-to-last line of dialogue is "I have a plan!" Too late, Doctor.

There's been endless analysis of this ending. Some critics think that Strangelove's "resurrection" means that fascism wasn't dead, after all—it was just temporarily disabled (the wheelchair). If Strangelove's right arm represents the Fascist tendencies he's trying to suppress, those tendencies win out in the end as he shouts, "Mein Fuhrer!" Even though the USSR and the US teamed up to battle the Nazis in WWII, the Nazis have the ultimate victory in this film. (Source)

Pretty deep. On the other hand, the original ending was going to be a pie fight in the War Room, until the Kennedy assassination made Kubrick re-think a scene with a President presiding over a totally ridiculous situation. So maybe it's all just a big joke.