Typically, Swordsage maneuver recovery will not be interrupted in the normal course of combat.
You ask:
Does taking damage before the start of your next turn interrupt the meditation?
This suggests to me that you're expecting to treat the Swordsage's maneuver recovery action the same way you would treat a spell with a casting time of 1 round, which does work this way. From the SRD's section on spell descriptions:
A spell that takes 1 round to cast is a full-round action. It comes into effect just before the beginning of your turn in the round after you began casting the spell. You then act normally after the spell is completed.
A spell that takes 1 minute to cast comes into effect just before your turn 1 minute later (and for each of those 10 rounds, you are casting a spell as a full-round action, just as noted above for 1-round casting times). These actions must be consecutive and uninterrupted, or the spell automatically fails.
When you begin a spell that takes 1 round or longer to cast, you must continue the concentration from the current round to just before your turn in the next round (at least). If you lose concentration before the casting is complete, you lose the spell.
However, those rules are specific to spells with a casting time of 1 round. They are not generic rules for all full-round actions. The rules for full-round actions (also from the SRD) say the following:
A full-round action requires an entire round to complete. Thus, it can’t be coupled with a standard or a move action, though if it does not involve moving any distance, you can take a 5-foot step.
And that's it. Unlike casting a spell with a casting time of 1 round, there's nothing about needing concentration checks, or waiting until the beginning of your next turn to take effect. Normally, full-round actions work just like other actions (standard, move, or swift), and take effect at the conclusion of the action. The only thing that's special about them is that they take up all of your actions on your turn (aside from 5-foot steps and free actions).
So, under normal circumstances, using a full-round action on your turn to recover your Swordsage maneuvers will not provide an opportunity for interruption. The action will resolve on your turn, and does not provoke attacks of opportunity, so most of the time you just take the action, it resolves, and nothing else happens. Taking damage (or anything else) prior to the start of your next turn doesn't matter, because the action has already resolved.
It is possible for Swordsage maneuver recovery to be interrupted, if an enemy has a way of acting during your turn and preventing you from taking actions.
You also ask:
Is it interrupted by getting stunned or something?
This is getting at the case where Swordsage maneuver recovery can be interrupted.
If an enemy has some way of acting during your turn (say, they took the Ready action on their own turn prior to yours, or are capable of casting the Celerity spell (SpC, p. 271) as an immediate action), then they might be able to preempt your full round action. If they do that, and then use their action during your turn to do something that prevents you from completing the action (like inflicting the stunned condition), then that will indeed interrupt your maneuver refresh.
Note that only doing something that specifically prevents you from taking actions will work for this. If they simply deal damage to you, that won't interrupt the maneuver refresh; the rules about concentration checks when taking damage and so on are specifically for spells, not generic rules for all actions.
