The more important part other posts haven't touched on is that he is the one who crippled the traveler. Rasputin activated a plan called operation ikelos where he killed off the entirety of the human race except those directly under his protection which happened to be the city in Russia nearby, soon becoming the last city. The reason behind this is unclear and perhaps it wasn't all of humanity but we know the count was in the billions. The reason for this is that he didn't want the darkness (we'll assume) taking over the humans or risking that it would. He also crippled the traveler because he knew everything around it was safe (so we assume). There's a few theories that the traveler itself was evil but what we know for sure is that the traveler abandons every race it visits, thus it's name. It constantly travels around. Rasputin knew that if the traveler left earth, humans would share the same fate of the fallen IF they were lucky to survive at all. So that huge blown up bottom portion of the traveler is thanks to rasputin Rasputin has a current protocol called midnight exigent in progress and we don't know too much about it. What we do know he's currently doing is learning. He's watching everything everywhere, learning from all the enemies, the traveler, etc. he's trying to become an all knowing ai that can actually beat the darkness since thats the one thing he couldn't predict and anticipate the motives of. Midnight exigent, his current protocol, basically means the darkness is his main concern. Exigent means very demanding and midnight is usually around when its darkest out so "dark important" is kind of what it translates to. His full history and what he's planning to do fully are just another part of destiny left unexplained for now. He's definitely going to play a large role going forward

I'll give you the abridged version Rasputin and his cousins (or brothers and sisters - not clear if they're the same thing) were built to defend Humanity and the solar system by using of doomsday weapons. He detected something just outside our planetary system that was driven and inimicable. When it entered out solar system, he took control of all defences and attacked IT. He attacked and those doomsday weapons proved useless. He then shutdown all defences and then shut himself down, leaving humanity undefended. After the collapse, he was just a myth to most people. Someone entered his bunker and brought him out of hibernation. Since then he's been pretty incompetent and had his main bunker and core invaded by both Fallen and Hive/Taken. At one point he squealed like a little girlie for help, on an open channel, all across the cosmedrome. In a nutshell, that's about it.