Until May 15, you can hold as many acceptances as you'd like. Many, if not most, schools will ask that you respond within 2-4 weeks of their accepting you to tell them if you'd like to keep your spot or decline the acceptance. Also, most schools require a deposit (usually only $100 or so) to hold your spot. But if you withdraw an acceptance before May 15 your deposit is usually refunded. By May 15 you must be holding only one spot, hopefully at the place you want to go anyway. So, long story short, many people hold multiple acceptances up until May 15th.
After May 15, you can still be on multiple waitlists while holding your one acceptance. At this point, you usually only have 1-2 weeks to decide to take an offer if accepted off of a waitlist because it's kind of the scramble time for schools to fill their class from the waitlist. I'd say only a minority of people have to worry about this, most people know for sure where they're going on or before May 15, but if you're on the waitlist for places that you'd rather go over where you've already been accepted, or if you are only on waitlists and have no definite acceptances, it can be stressful.
Hopefully this makes sense, good luck!
