an accept state
An accept state is a state that means 'yes' — if the machine has finished reading the whole input and it is sitting in one of these states, the verdict is accept. In the diagram an accept state is drawn as a double circle; in the five-tuple the accept states are the set F (a subset of Q, possibly empty, possibly all of Q).
The crucial detail beginners must internalise is that the accept/reject decision is made once, at the very end, based only on the final state. Passing through an accept state in the middle of the run means nothing; what counts is the state you are in when the input runs out. A string is accepted precisely when its run ends in F, and rejected otherwise. Visiting B then leaving it does not earn acceptance unless you happen to be back in B at the end.
Which states you mark as accepting is a design choice that completes the specification. The states track the facts; F selects which combinations of facts you are willing to call success. The 'ends in 1' machine, the 'divisible by 3' machine and the 'even number of a-s' machine can share the same states-and-transitions structure as some other language and differ only in which states sit in F.
On the parity machine for 1-s, choosing F = {Even} accepts strings with an even number of 1-s, while choosing F = {Odd} (same states, same δ) accepts strings with an odd number of 1-s. Only the set of accept states changed.
Acceptance is decided only by the final state; mid-run visits to F do not count.
F may be empty (the DFA then accepts no string at all, recognising the empty language) — this is perfectly legal and different from accepting only the empty string ε.