Xenophilius is an interesting dude—with a very interesting fashion sense. He and his daughter, Luna, are known for being a bit quirky and believing in stuff that other wizards don't—you know, certain magical creatures, secret conspiracies, etc.
Sure, a lot of people think the Lovegoods are kooks because of all that, but the upside? They're extremely open-minded and independent people, and they so they're good at thinking for themselves, giving people and ideas the benefit of the doubt, and the like.
So, for example, Xenophilius has been using his newspaper, the Quibbler (which is basically the National Inquirer of the Wizarding world) to drum up support for Harry and make sure the truth about Voldemort's return is out there. This is pretty important work, since the more mainstream Wizarding paper, the Daily Prophet, has increasingly become a propaganda arm for Voldemort/the Death Eaters.
Unfortunately, Xenophilius is human, too—so when the Death Eaters kidnap Luna to punish him for his acts of journalistic resistance, he's so desperate to save her that he tries to turn Harry in in the hopes of getting his daughter back. You see, Harry and the gang go to Xenophilius to get some important intel about a symbol they keep seeing, and X is happy to get into tons of detail about the history of the symbol…so he can keep them there until the Death Eaters can arrive.
When Harry tries to leave, he panics:
XENOPHILIUS: You're my only hope. They were angry, you see, about what I'd been writing. So they took her. They took my Luna. My Luna. But it's really you they want.
HARRY: Who took her, sir?
Harry and his friends escape, but we have to say, we lost a little bit of respect for old Lovegood as a result (though, in fairness, we get that he was trying to save his kid—we have to cut him some slack on that front).
Oh, and he did serve a very important role in the story: he gave Harry, Hermione, and Ron the skinny on the Deathly Hallows. Ron and Hermione had heard "The Tale of the Three Brothers" before, but what they didn't know is that some folks think it wasn't fiction. Xenophilius is among the believers, and he tells the kids that there are three objects out there that, when possessed together, make you the master of death.
Now, the kids still think Xenophilius is a little bit, er, eccentric. And they don't necessarily believe that this children's tale could be real. But, as you'll see in the next film, the potential that these magical death-mastering objects could be real is a game changer. So, hat tip to Xenophilius for clueing everyone into their significance.
(Oh, and Luna does escape the Death Eaters—Harry gets her out of Malfoy Manor when he accidentally gets trapped there.)