Ramsay marries Jeyne to solidify a claim to Winterfell and forces Theon/Reek to confirm in front of the rest of the Stark bannermen that Jeyne is actually Arya (even though Theon also knows damn well she isn't).
Now, on the show, viewers got mighty pissed over Sansa and Ramsay's "wedding night" and how it was yet another example of how tasteless and exploitative the show has become in its constant portrayal of sexual assault. This is a 100 percent accurate interpretation, but it is our duty to inform those of you who haven't read the books that Ramsay's wedding night was mind-blowingly worse in George "Mixmaster" Martin's original text:
"No." Lord Ramsay poured himself a cup of wine. "Laces take too long. Cut it off her."
[...] Finally the gown fell away, a pale tangle round her feet. "Her small-clothes too," Ramsay commanded. Reek obeyed.
[...] Ramsay rose, the firelight shining on his face. "Reek, get over here. Get her ready for me."
For a moment he did not understand. "I ... do you mean ... m'lord, I have no ... I ..."
"With your mouth," Lord Ramsay said. "And be quick about it. If she's not wet by the time I'm done disrobing, I will cut off that tongue of yours and nail it to the wall."
Somewhere in the godswood, a raven screamed. The dagger was still in his hand.
He sheathed it.
Reek, my name is Reek, it rhymes with weak. Reek bent to his task.