The Blitties are a species that appear in Mario & Luigi: Bowser's Inside Story. They are animate blocks that resemble cats. Broque, after meeting with Bowser in Dimble Wood requests that Bowser locate & bring him these "rare creatures". They're trapped within enemies during battle, so Bowser must use his Vacuum command to obtain them as an item. There are 15 Blitties in all.
Once Bowser gets them, he can go to Broque's shop and leave them there. He gets extra equipment for that. The reward for finding all fifteen Blitties is a new special ability for Bowser, Broggy Bonker.