What does the term "carebear" mean in Eve Online?

Solution 1:

A "Carebear" is a derogatory term used for characters who stay mostly in Concord (police) controlled space and never ventures into unsecured "0.0" space.

Basically synonymous to cowards.

Solution 2:

This term spans wider than Eve. Urban Dictionary defines "care bear":

1. 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.

Solution 3:

A carebear is someone who avoids pvp. Quite frankly, I'm a carebear, but I live in nullsec areas, I just run away and hide, and only go where no one else is.