Overwatch will deputize some players as "investigators" (based on stats like wins and hours played), who are then given a replay of a match from a reported player, and asked to rule on whether "the suspect" was cheating, griefing, or if there's "insufficient evidence" to rule. Once a collective verdict is reached, Valve will then determine if a ban needs to be given, and investigators will be rewarded if their judgments all agree.
The process sounds very much like League of Legends' Tribunal program, which Riot Games has been using recently to try and cure that game of toxic player behavior. Valve says the system is currently in beta, and that it will be adding test cases to make sure the program works correctly. Eventually, however, the plan is to make Overwatch completely driven by the community.