Pittsburgh has had nothing but woes with their backstops. Ryan Doumit hit the DL earlier this season, which was the first blow, given his decent batting numbers (113 wRC+ - suggesting he's about 13% above the average batter). Chris Snyder looked similarly solid (116 wRC+) before undergoing back surgery. Pittsburgh traded for Boston's Michael McKenry (the same as the one who used to play for the Sky Sox) and has played 7 different catchers this season alone.
Cleveland's situation is less dire, as Carlos Santana is a fine catcher and Lou Marson, while nothing flashy, is a fine backup. Acquiring Iannetta would allow the Indians to leave a steady catcher behind the plate, avoid injury to Santana (who had his knee wrecked in 2010 during a home plate collision), and upgrade their 1B bat by leaving Santana there more often (Matt LaPorta's 96 wRC+ leaves something to be desired).
While losing Iannetta would surely be another hit to the Rockies' lineup, it wouldn't really impact the ultimate end to the season - missing the postseason. Instead, if a trade were to happen, the Rockies would be able to give top catching prospect Wilin Rosario a shot in the majors, or perhaps even Jordan Pacheco (who may be more of a 1B/3B/C type of utility player).
Iannetta, 28, is doing a solid job as Colorado's primary catcher, posting a 115 wRC+ on the season. Iannetta is in the 2nd year of a 3-year, $8.35M contract with Colorado. He has had a career as a roughly MLB-average bat (102 wRC+), but has drawn a lot of short straws in catcher competitions over the past couple of years, losing the starting role to Yorvit Torrealba and Miguel Olivo at different points.
Don't expect this to be the only potential move you hear about involving Colorado, as several other players are candidates to be moved this deadline.