From the Super Mario Wiki
The Blitties are a species that appear in Mario & Luigi: Bowser's Inside Story. Their name is a combination of the words "block" and "kitty". 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. They are always trapped in the first enemy group of that species that Bowser encounters. If Bowser fails to suck up the Blitty, the Blitty gets trapped within the second enemy group of that species that Bowser encounters.
The reward for this side quest depends on how many Blitties are collected.
| Number of Blitties
|| Block Band
|| Block Fang
|| Block Ring
|| Broggy Bonker Special Attack
Names in Other Languages
|Blocat, portmanteau of English block and cat.
||Pun on Bloque (Block) and miau (meow).
||From Gato (Cat) and bloke, corruption of bloque (block).
||Pun on Bloc (block) and minou (cat)
||Pun on chat (cat) and bloc (block)
||From Block (block) and Katze (cat)
||"Fufi" is the most common cat name in Italy, while "Blocco" means block