League Of legends Wiki - Roles - The Feeder
If a champion gets killed repeated thereby often more damaging to the team than a summoner who leaves the game or does nothing at all.
Feeding can also be a passive act. If several players die to one champion, it will gather high amounts of gold, the fed champion will more likely be able to defeat single champions in the future.
A champion is considered to be "fed" as soon as his potential to be useful in game and to score kills is obviously significantly higher than any other champions.
This can occur independently from a high champion kill-to-death ratio, as minion and monster kills also generate gold.
Carry champions (ADCs - Attack Damage Carries and APCs - Ability Powered Carries) profit most from being fed, since their strength in game massively depends on the items they have.
Feeders do not necessarily assist the enemy team intentionally. Players who are new to the game and thereby lack experience tend to die more often and more easily to skilled players.
Feeding is also a vicious circle. Every time he kills, the killer gets stronger and is thereby even harder to defeat next time.
This may result in a spiral downwards where the gap between the champion levels and equipment becomes wider with each kill, and thereby diminishes the chances of the killed champion to get back on the level of the other champions.