A trading position is considered to be covered if it is offset by another position. In other words it is a synonym for hedged but usually only in the the context of trading and arbitrage.
The opposite of covered is "uncovered" or "naked".
A covered position is usually much less potentially profitable than a naked one, as the hedge either creates an offsetting loss (e.g. if covered by a future) or a cost (if covered by an option). The usual correlation between risk and return holds!
A perfectly covered position cannot make a profit greater than the risk free rate unless it exploits an arbitrage opportunity, as in Covered interest arbitrage.