Not to forestall further (in-depth comprehensive) answers, but there's a section of our Frequently Asked Questions page about the Sea People featuring not only a great explanation of where the term 'Sea Peoples' comes from, and why it isn't that mysterious by /u/bentresh and a good summary of what we know about the phenomenon by /u/kookingpot, but also an AMA with the author of 1177 BC: The Year Civilization Collapsed.
/u/bentresh gave an excellent reply to my question about the same time period here just yesterday. I didn't ask specifically about the Sea Peoples because most scholars view them as one among many factors leading to the late bronze age systems collapse, but his reply is possibly of interest to you as well. In agreement with others, I think Cline's book 1177 BC is a highly approachable book that's very interesting and I talked about it with my friends for weeks after reading it.
My response in the FAQ focuses primarily on the Philistines. I recently wrote more about the Lukka and Eqwesh, two of the other groups, in What do we know about the so-called Sea People's origins?
I answered a follow-up question here about why I don't think the term "Sea Peoples" is a useful one.