The system is part of Riot's ongoing effort to promote good behaviour amongst its playerbase. Jeffrey Lin (Lead Game Designer of Social Systems at Riot - i.e. in charge of creating and tinkering with player behavior systems) explains that speed is important when responding to abusive outbursts or bad behaviour in-game: "we know that the faster a player receives feedback, the better their chances of reforming."
The tests for the EU region started Friday and they're being geared towards verbal harassment. That means homophobia, racism, sexism, death threats and the like. If a report is validated the system then works out which punishment is appropriate - Lin mentions two-week or permanent bans as the options in his explanation. The system then sends the offending player a reform card via email pointing to the problem content in the chat logs (with other people's data removed) and officially notifying them of the punishment.
These systems aren't fail-proof - I think a previous situation with LoL punishment systems had a guy banned for flaming and it turned out he was actually beating himself up in chat, so banned for flaming himself - so Riot have said they'll be "hand-reviewing the first few thousand cases". Depending on whether the system proves reliable or not, the plan is to roll it out across other regions.
Though the reform system is starting out with a very stick-centric approach, carrot could be added in at a later date with the potential for swift rewards after some top behaviour. Chat restriction, removal of ranked queue access, and ability to pick out jerk gameplay like intentional feeding are also in Riot's sights as possible additions to the Justice-o-tron.
I mean, I assume they are calling it the Justice-o-tron. Why wouldn't they be?