I've recently re-activated my account. I've seen this term used in the online chat and wondered what it means.
This term spans wider than Eve. Urban Dictionary defines "care bear":
- Lightly derogatory term for an MMO player who avoids PVP combat, heavily preferring cooperative or solo PVE combat, chatting, or developing tradeskills/running quests. Depending on the game and the individual, this PVP avoidance can show up in several ways: by playing on strict non-PVP servers; by avoiding PVP areas or declining duels; or, by avoiding or condemning PVP players.