Henrik turns 82 years old on the first page of the book. He's a widower and was married to a Jewish woman he helped escape Germany during World War II. This earned him the scorn of his three Nazi brothers, two of whom are now dead. He's owns most of Hedeby Island and is current patriarch of the Vanger clan. In some ways, he's at the very heart of The Girl With The Dragon Tattoo, being somehow connected with each of the novel's various spheres and themes. If it wasn't for him, the worlds of Blomkvist and Salander might never have collided.
He's also a somewhat suspicious character. Why is he so obsessed? What's with this guy? Until we know the truth, we might suspect him of being behind Harriet's disappearance, or of setting Blomkvist up for something. His shiftiness deflects attention from Martin, the real bad guy here. He shrewdly manipulates Blomkvist, seducing him with money, revenge on Wennerström, and the sheer intrigue of the Vanger family.
It turns out that Henrik is a basically benevolent figure, a kind man whose heart was broken by the loss of his grandniece, taking one last stab at the truth before he dies. It's never exactly clear why he's so convinced Blomkvist is the man for the job or the man to hear his story. He also uses Blomkvist as a confessor. After all these years, he needs someone to unload his secrets on. He wants to talk about his Nazi brothers, and he wants the mystery of Harriet to be solved. He also wants to get revenge on whoever killed Harriet and whoever is sending him all those flowers.
The big question is, did Vanger ever really intend for his biography/autobiography (it's not quite clear what he intends the book to become) to be published? What would be his motivation? If it turned out that Martin did kill Harriet, would Henrik want it public knowledge that Martin and Gottfried were serial killers? Regardless, if Martin hadn't killed himself, Henrik wouldn't have had a choice in the matter.