The wife and child of Detective Max Payne were murdered. He arrived home in time to kill two of the culprits, but the third escaped and was never found. Payne transferred to cold cases, and uses his now-copious free time to try and hunt down the final killer.
And then suddenly there are fresh bodies turning up, and Max finds himself the number one suspect because these are film-and-TV cops and therefore if they aren't protagonists they're idiots.
Wikipedia reports that star Mark Wahlberg said of his title role in this film that it was "all driven by emotion". And he may very well have said it, but you certainly won't see that on the screen. Wahlberg is stoic to the point of being comatose for pretty much the whole duration of the film. I can't say I blame him: it felt like the movie was trying to put me to sleep, too.
Max Payne is a dumb action film, with a nonsensical plot and secondary characters that exist only to perform narratively useful actions at the times the script needs them to. And honestly, I could forgive all that stuff if it wasn't for the fact that it is also boring.
If you simply must watch a gun-happy action film based on a computer game I didn't much like, watch Hitman instead. At least the main actor there seems to be awake.