Some TMNT stuff really isn't for little kids.
Splinter is a mutant rat who is the sensei and father of the Ninja Turtles. His background seems to be similar to that of the IDW series' Splinter, being a former rat who is also referred to as "Hamato Yoshi."
Along with his four sons and his nemesis Shredder, he was thrown into a different dimension by the alien warlord Krang. Once there, Splinter and his sons took refuge in the sewers, until they clashed with Batman. Splinter kept the superhero at bay until his sons could retreat, then made his own escape. However, he followed Batman to a laboratory, discovering the effect that this dimension was having on the mutants, reverting them back to base animals.
He then led his sons to the Batcave, and revealed their history and reason for being there to Batman. Batman and the family joined forces and attempted to return them back to their own dimension, but they were thwarted when Shredder maliciously destroyed the teleporter.
After this, Splinter returned to the Batcave, where he oversaw Batman's martial-arts practice with Leonardo. He was given the choice to return with Casey Jones to his home dimension, but chose instead to save Batman from an onslaught of mutant Arkham Asylum residents. Casey and April O'Neil then returned to Batman's dimension, allowing Splinter and the Turtles to return.
Splinter encountered Batman again sometime later, after his son Donatello accidentally sent Bane to their dimension, causing mass chaos. He, his sons, Batman and Damian Wayne all attempted to ambush Bane, but Splinter's rescue of Raphael led to him being attacked by Bane and severely injured. He was left in a coma, barely alive.
Raphael and Batman's cohorts then took Splinter to a Lazarus Pit to be healed, and a newly revitalized Splinter took out his aggression on the Ninja Man-Bats. He returned to his own universe then, and joined Batman and Shredder in their battle against Bane.