It's always difficult to extract the fact from the fiction when dealing with the Norse heroes. Ivar exists right at that point where the sagas are crossing over into the more reliable histories laid down by the Saxons, and I'm going to try sticking to what I consider to be the most realistic account of his life.
He was, we are told, the second son of Ragnar Lodbrok- king of the Danes. Ragnar is a figure so wrapped up in the sagas that some query whether he can be considered a historical character at all, but I'll give him the benefit of the doubt. He was an inveterate raider, who finally met his match at the hands of the power king Aelle of Northumbria around 863AD. We are told that Ivar was born in 794AD, which I find impossible to believe, as it would have made the raidin', brawlin' Ragnar Lodbrok about 90 years old at the time he was attacking York. I would consider a birthdate of around 820AD far more realistic.
At that time, Ivar was based in Dublin with his ally Olaf the White, the Norwegian king of the Irish colony. Also with them was Ivar's younger brother Halfdan. The Danish brothers used their alliance with the Norwegians to lead numerous plundering raids along the coasts of Ireland, England and Scotland, but didn't appear to have have interest in conquering or colonising at that point.
So who was Ivar? Much of the study of his character revolves around his curious nickname, which has spawned many theories. Some have speculated that it was because he was very tall; others feel it was because he was very thin. Some have suggested it was due to impotence, whilst others speculate on a cunning "snake-like" personality. However the most popular theory is also the one that at first seems most unlikely, and is also the one I subscribe to. I believe that Ivar was a cripple.
Specifically, he was afflicted by a form of brittle bone syndrome affecting his legs- leaving them twisted and apparently boneless. Some sources state that he couldn't walk. Vikings sometimes euthanised crippled children, but coming from a prominent family may have ben the reason why Ivar lived. Amazingly, he became a famous warrior- the tales recount him being carried into battle on a litter by slave, for him to fight with bow and arrows (he was a lethal and famous archer).
Up until 863AD, the Vikings hadn't gone in for colonising mainland Britain much, although they had seized chunks of Ireland. That all changed after the death of Ragbar Lodbrok (the tradition being that he was thrown into a pit of adders, which strikes me as highly unlikely). Spurred on by the execution, Ivar and Halfdan raised a large army- "the Great Host"- and invaded East Anglia.
This was something new for the English. This wasn't a raiding party- it was a huge and well-organised invading army bent on conquest. The once-strong kingdoms of Northumbria and Mercia had been weakened over the past century, while the emerging Wessex had not yet managed to consolidate its position. From his East Anglian base, Ivar struck to the North, capturing York in 866 and the kingdom of Deira. He didn't bother to rule it- that just wasn't his style at all- but installed a terrified Egbert as client king while planning his next move. Over the next few years he ravaged the whole east coast of England.
In 870 AD he pulled off an even more daring victory. The kingdom of Strathclyde was an independent kingdom populated by an ethnic mix of Picts, Britons and Dal Riatan Scots, dominated by the fortress of Dumbarton which was one of the most powerful strongholds in the British alliance. Alongside Olaf the White, Ivar forged anunlikely alliance with Constantine, king of Scotland, and invaded Strathclyde. Eschewing notions of siege tactics, Ivar simply stormed Dumbarton in a head-on assault with berserkers. It was the first time Dambarton had ever been captured, and Strathclyde fell.
Although he was acknowledged as the main leader of all the Vikings in the British Isles, Ivar still held no kingdom of his own. That changed in 871 when Olaf the White returned to Norway. Ivar set himself up as king of Dublin, and set about quelling the rebellious neighbours. There are various stories surrounding his death in 873- the most likely explanation being that he was killed in a minor raid. His descendants went on to become the dominant Viking rulers in Britain in his almighty wake.