An agency sends you an offer for a gig. You'll get a notification, and it appears in your offers list with the venue, date, times and fee.
Accepting creates a booking. That's a commitment: the venue is told, and the agency stops looking for someone else. You'll be asked to agree to the booking terms before it goes through.
Declining tells the agency you're not available, and they'll offer it to someone else. Declining costs you nothing and is much better than silence.
Offers don't stay open forever. If a gig's date passes, or the agency fills it another way, the offer closes.
If you're offered a run of dates, a residency, you can accept the whole run in one action. You're accepting a separate booking for each date, on the same terms, so check the list before you tap.
If a date in the run clashes with something you've already accepted, that date is skipped and the rest go through. You'll be told how many were taken.