The trade that necessitated this move (the acquisition of Brent Lillibridge) is covered here.
Added UT Brent Lillibridge to the 25-man Roster
Designated OF Aaron Cunningham for Assignment
The Indians upgraded their 25-man roster by adding a player in Lillibridge that complements the offense-first games of Shelley Duncan (who can only play a corner) and Jose Lopez (who can't play short and shouldn't be playing second). Lillibridge can cover both center field and the occasional start at second or short, and still give Manny Acta the defensive replacement he likes to have for Damon or Duncan in the late innings when the team's ahead.
As for Cunningham, I'm going to play devil's advocate for a bit.
Aaron Cunningham's role on this club was a very difficult one; he would play almost every day, but often only on defense. Usually the timing when the offense-for-defense switch occurred was based on when Damon or Duncan's next at-bat fell. If Damon/Duncan made the last out of the sixth, Cunningham would go in in the top of the seventh (if at home); he'd usually go in an inning later in a road game. The point is that Acta was trying to maximize the at-bats that Damon/Duncan were getting while at the same time maximizing the number of defensive innings Cunningham was playing. While this made for sound baseball strategy, it really hurt Cunningham's offensive ability, for he'd at times go several weeks with no more than one at-bat in a game, and those at-bats were usually against late-inning relievers.
So Cunningham was in an almost impossible situation in which to gain playing time, as unless he happened to get to hot for one at-bat in consecutive games, he wasn't going to get many starts. This became true especially after Johnny Damon came aboard, for that made him third on the left field depth chart, with the other two positions being covered with players who rarely were given days off. But Cunningham was shunted into this position because of option status (not really his fault) and his poor performance in spring training, which he had control over. With a good spring, he could have won the left field job, or even have taken some early-season at-bats away from Michael Brantley. But he didn't so Shelley Duncan won the left field spot by default, and Cunningham was reduced the role he filled up until today.
Because he can't be optioned to AAA, it's going to be a tough sell for another major-league club to put a waiver on him. In fact, I think it might be best for his career for him to pass through waivers, be outrighted, and finished up the season playing every day (or at least regularly) in Columbus. He can then be a free agent in the middle of October, and try to find the best situation for himself. A right-handed outfielder who can play all three spots is a niche role, but a role with which he could hollow out a career for himself. But he'll have to be able to hit, and hit after sitting for 3-4 days.