Yep, that's the epiglottis alright.
The uvula's functions are less clear, though it plays a role in speech in some languages.
I always thought it helped separate the saliva from the air passage but I am not told that in class. Maybe I made it up.
Having the uvula removed is horribly painful for an extended period. And you cannot bear to eat at all. Avoid it unless it's life/death.