The word "toxic" is usually used to describe the summoner and their actions; not the champion they are playing.
(From a previous post): ..."it used for a quite large amount of behaviors such as flaming, blaming and trolling.
The actions of a certain individual which actively or passively decrease the team moral and performance are considered toxic. A toxic person is also able to bring up negative behavior in other/neutral people.
A toxic environment results in less team-play and usually lost late-game as people distrust each other.
So basically toxic describes all possible offenses in one word."
Edit: Lyte, from Riot, said this in a 2013 post (http://www.reignofgaming.net/redtracker/topic/94110-who-invented-the-word-toxic)
"The reason we use the word 'toxic' is very intentional.
In our observations and research on player behavior, we find that a single source of negative behavior can ripple through hundreds or thousands of games. For example, let's say we have a game with 10 players--9 are positive, and 1 is negative. The 1 negative player is racist, rages all game, and intentionally leaves the game. This experience can negatively influence some of the other 9 positive players in the game. Some of these 9 players will play another game of League of Legends and instead of being positive, they might start the game neutral or negative. Their actions can then influence 9 other players in the game, and toxicity spreads.
A single negative action could result in thousands of games with negative incidences--this is why many of our latest experiments focus on shielding players from toxicity (Restricted Chat Mode -- forcing players to make a decision between using limited chat resources for cooperative communication, or still using it for negative purposes and being message capped), or stemming the spread of toxicity (our next experiment)."