According to Titans Online, the Rams are giving up two first-round picks (this year's and next year's), two second-round picks in this year's draft (43rd and 45th overall), and two third-round picks: this year's 76th overall pick, and the Rams' 2017 third-rounder. The Titans will also give up their 2016 fourth- and sixth-round picks.
That leaves the Rams with just five picks in this year's draft: the first pick, two fourth-rounders and two sixth-rounders. They're also short a second and third-round pick in 2017. If they don't get this pick right, they'll be completely talent-depleted in two years.
This is one of Titans general manager Jon Robinson's first big moves, after serving as the Tampa Bay Buccaneers' director of player personnel for two years.
It seems a foregone conclusion that the Rams are picking a quarterback with that pick, presumably Carson Wentz, which is both good and bad news for the Bucs. It means the Rams won't be trading for Mike Glennon, but it'll take another team out of the running for a top QB -- the Jets, perhaps -- and they might pull the trigger on a Glennon trade.
Moreover, this will push down the rest of the talent in the draft as well. The Bucs don't care about the quarterbacks in this draft, because they have Jameis Winston. So any team picking a quarterback ahead of them increases the odds of a top talent at another position falling to them -- the Bucs are particularly intrigued by Florida State cornerback/safety Jalen Ramsey, but it seems unlikely he'll fall far enough for Tampa Bay to have a shot at him. Ohio State defensive end Joey Bosa might be a more realistic target, though.