"Panem et circenses" is an old Latin (meaning Ancient Roman) say meaning that you can rule a population providing them with food and games (entertainment). If you do so, as a ruler, you will have them follow you, accept everything, and be happy. It is meant negatively to claim that most people do not have any bigger desire than to feed themselves and have some basic form of fun/entertainment.

It only applies to Hunger Games (movie - I haven't read the books either) partly, because the Circenses, the games, Romans had, involved slaves (so, non-citizens), people sentenced to death, war prisoners, or animals, so Roman people would actually not have their families at risk. Not that much, at least. I doubt they'd enjoy the games as much otherwise. Admittedly, being sentenced to death was quite easy.
Of course, if I remember well from school books.

As to the movie: it did not bug me much because, even if not so blatantly, it seems to me history is full of examples of cruel rulers pushing population to despair, causing revolts and violence and revolutions, only to crush them with even more violence. Until revolutions in 18th and 19th centuries (French, American, others throughout EU), when Democracies started to replace Kingdoms or other more or less cruel forms of gov't.
I mean, yes, the movie makes it all look more silly, I'd agree with that, but still, sadly, not so unreal if you look at even recent history.