It's not uncommon to provide a play synopsis if you're doing a play by Shakespeare (or one of his contemporaries) and you're worried that the audience might have trouble understanding all the details because the language is a bit tough for some people to understand. But if you're doing a play that's easy to follow, you really don't need to have a synopsis or overview at all. What for?
The one thing you could have, if you wanted to, would be a couple of words mentioning the time and place of the acts as well as info about intermission, e.g.:
Act I: New York, New Year's Day, 1983. Bob's Apartment.
Act II: New York, Jane's Apartment, later the same year.
There will be a 10-minute intermission after Act I.
In addition to cast and crew, you may also need a "Special Thanks" section for people who weren't a part of the production but who helped it a little somehow, i.e., by contributing a costume or set piece, driving students home, etc.
If you're doing a well-known play and you want to get fancy, you can devote a little space in the program to some insightful quotes that critics or scholars wrote/said about the play--but it's certainly not necessary. A lot of regional, (professional) non-profit theaters do that sort of thing; New York theaters usually don't. Similarly, sometimes regional theater programs will include a little note from the director or the head of the theater about why the play was selected for production, why it's a good play to do here and now, etc. Again, NY commercial theaters hardly ever do that, either. You could ask the teacher who picked the play if she/he wants to write a little paragraph about that.
Some programs let the cast and crew provide a little bio after their names, e.g.:
John Barrymore (Hamlet): This is John's fourth production at Westmore High. He has also acted in summer stock theater productions in Phoenix and... (blah blah blah)
I would advise against doing this because people get a little self-indulgent and it's really not necessary. If you do include a section like that, make sure you set firm limits about how long a bio can be--two or three sentences should be enough--and don't let people "give a shout out" to three dozen friends and their extended family! Otherwise the program will be 20 pages long!
Break a leg...