Does damage marked on a creature reset at the end of each turn or remain until the cleanup step?

Marked damage on a creature is removed during the cleanup step, which is the final step of the ending phase. This is governed by CR 514.2, which states that damage marked on permanents is removed and 'till end of turn' effects expire simultaneously during cleanup.

It is important to note the distinction: damage does not reset 'at the end of turn' (which refers to the end step, a different part of the turn). The cleanup step comes after the end step. So if something deals damage to a creature during the end step, that damage is still removed before the next turn begins.

Until that cleanup step occurs, damage accumulates on a creature throughout the turn. A creature with 2 toughness that takes 1 damage in the first main phase still has that 1 damage marked on it during combat — meaning 1 more damage is enough to destroy it via lethal damage (CR 704.5g, the state-based action that destroys creatures with damage greater than or equal to their toughness).

Example: Your opponent's 2/2 creature blocks and takes 1 damage in combat. Later in the same turn, you cast a spell that deals 1 damage to it. State-based actions check and see it has 2 damage marked against 2 toughness — it is destroyed. Had the turn ended and restarted, the first 1 damage would have been removed in cleanup, and the second 1 damage alone would not be lethal.

So practically, each new turn begins with a clean slate because of cleanup, but within a single turn, damage is cumulative and can matter a great deal for combat math and removal sequencing.