After Morgan's (Lennie James) son Duane (Adrian Kali Turner) is bitten by his zombified mother, Morgan becomes something of a rage machine, killing harmless passersby as mindlessly as walkers. Only meeting Eastman brings Morgan back down to earth, transforming him into the character The Walking Dead fans are most familiar with.
Eastman has a troubled pre-apocalypse past himself. After his own family was slaughtered by a psychiatric patient of his, he took justice into his own hands, starving the murderer to death in a homemade cell. Eastman's regret drove him to seek a more peaceful lifestyle, leading him to practice aikido and swear to never kill anyone again. Passing these lessons onto Morgan is Eastman's way of assuring the path of non-violence doesn't die with him. In his purview, even walkers deserve a degree of respect; he makes a habit of digging and marking graves for them after putting them down. Ironic, then, that Eastman dies protecting Morgan from a walker.
So, where do the TMNT factor into this? Well, Eastman is actually named for Kevin Eastman, co-creator of TMNT alongside Peter Laird. A common name though it may be, the reference makes more sense when considering the t-shirt Eastman's wearing when out practicing aikido with Morgan one day, which has a turtle on it and says "Save Terrapins."
What really confirms the connection, though, is Eastman's weapon of choice: a staff, the same weapon used by Donatello. The smartest of the group, Donatello relies on his wits and know-how to get him out of a pinch more often than brute strength, though he's certainly no slouch with the staff he wields. Eastman's path of wisdom and compassion isn't exactly the same, but he's obviously someone who puts brains before brawn — or, at least, thinks brawn is nothing without brains to back it up. It wouldn't be a stretch to imagine the two characters getting along, exchanging knowledge and training in the way of the staff.
Eastman's existence is one of many Easter eggs on The Walking Dead, though a TMNT reference is certainly among the most unprecedented.
