Hi Claudia,

Although "ressortir" and "repartir" can have similar meanings, they are not exactly synonyms, and there is a subtle difference.

"Ressortir": to go out again (implying that you are going out of a specific place)

For example: Je ressort acheter du café (I' m going out again to buy coffee) 

"Repartir": to get going again, to set off again (implying that one was in movement, stopped, and is going again), OR, to leave a place to go back where we're from.

For example: Après une pause, il est reparti (After a break, he got going again) 
Tu repars déjà chez toi? (Are you going home already?)

I hope this helps!