Honor is "not a currency," says Riot (and it can't be traded or spammed), but it will be used to recognize worthy players over time, and the company says it is looking into possible "bonuses for the most Honorable summoners." For a long time, League of Legends players have been able to "report" each other for negative actions like being offensive or leaving a game early, but Honor seems designed to go the other way and reward positive actions instead. It remains to be seen how it will play out in the future. Riot is experimenting here, to see how players use the system before it's fully implemented.
Valve's Dota 2 also has some innovative social features planned, including a reward system like this for working together with other players in the game. These MOBA games are very complicated to play, and so companies like Riot and Valve are doing their best to get players to work together and create a solid community, rather than lose new players to widespread offensive behavior.