The team already had Drew Stubbs and Michael Brantley, two competent center fielders, under contract for this year, but Bourn is better than either of them and takes over the center field job, pushing them to left field or the trade block. Assuming no one is dealt, this probably pushes Nick Swisher to first base, hurting his value slightly, and Mark Reynolds to DH, which does the same.
Bourn's worth several wins a year above a replacement-level player -- again due to a huge boost from his plus-plus defense -- but in Cleveland's case, he's not actually replacing a replacement-level player, so he's probably not going to deliver more value to the team than they're paying him to provide. It's a reasonable contract (four years, $48 million), a year longer than you'd like for a speed guy entering his 30s, but very fair for the club considering the rate of acceleration of salaries this winter.
What I don't see here is the endgame for Cleveland. The team still isn't good enough to catch the Detroit Tigers without a substantial amount of luck in both directions -- bad for Detroit and good for Cleveland -- because the Indians lack the pitching to challenge for the division.
The club's starters had a 5.25 ERA last year and the only addition is rookie Trevor Bauer, who has great promise but who isn't likely to bring that figure down much by himself. To make their offseason acquisitions of Bourn, Swisher, Reynolds and Stubbs make any sense, they need to deal at least one of their surplus outfielders -- Stubbs or Brantley -- for pitching help.
They're not a .500 team as currently constructed, even with improvements on offense and in their outfield defense, even if you assume that one of Carlos Santana, Jason Kipnis or (least likely) Lonnie Chisenhall takes a step forward. In fact, as good as Bourn is, Brantley actually had the better triple-slash line last year while playing in the better league, although he can't touch Bourn on defense or on the bases.
The only other explanation for their signings this winter is that they're stockpiling assets that they believe will appear underpriced a year from now, and will thus be valuable in the trade market -- and they may be right, as neither Swisher nor Bourn signed for as much money on a per-year basis as we might have expected in a high-inflation market. It's possible that this will all turn out to be very clever on the part of their front office, but it may not prevent an 85-loss season in the meantime. Cleveland also loses the 71st overall pick, a competitive balance lottery pick, because heaven forbid we give the lowest-revenue clubs any sort of advantage in the primary way to acquire talent cheaply in this game.
The losers here are the New York Mets and possibly the Kansas City Royals. The Mets supposedly wanted Bourn but refused to give up their first-round pick -- the 11th overall selection -- which was left unprotected when both sides fell asleep during that portion of the last CBA negotiations. They're now left with an outfield, from left field to right, of Wynken, Blynken and Nod, which may be among the worst in modern major league history, even considering Nod's strong throwing arm and Blynken's tremendous batting eye.
The Royals, on the other hand, are somewhat dependent on the weakness of their division to make a run at a wild-card spot, so every move that Cleveland, Minnesota or the White Sox make to get better hurts the odds of Kansas City getting to the 88-win territory. There's nothing the Royals can do about this, but I imagine the hope of a fairly weak schedule helped them feel confident in trading Wil Myers for James Shields and Wade Davis -- a schedule that has become slightly less weak since that trade.