The Honor system in LoL is being reworked later this year to make it more meaningful. Introduced as a way to highlight good sportsmanship, it's just not being used in the ways Riot had hoped, so they're taking another look at it.
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Honor allows players to give other player a thumbs up for good behaviour. It's supposed to encourage more of this behaviour, but currently it's not having the impact it was supposed to have.
In a recent developer video, embedded above, Riot explain why they need to tweak it. "The current Honor system lacks depth and does a poor job of reinforcing sportsmanship," says lead producer New001. "It's hard to understand how the rewards work, and feedback can feel delayed or disconnected from your actions. At the end of the day, it just isn't super meaningful."
The new system will be better integrated into the mechanics of the game, say Riot. Perhaps we'll see some Dark Souls-esque emote etiquette find its way into the MOBA, or something similar.
Whatever the new system is, it will hopefully be backed up by the right incentives to keep players using it correctly.
Cheers, Dot eSports.