When is Dúnhere considered to be attacking alone?
Lets have a look at the rules. In the combat phase, after resolving the attacks by encountered enemies, it is the players turn to attack with hers/his heroes and allies. To attack a target the player declares the attackers and exhausts them. Then the combined attack strength will be determined and so on. Only encountered enemies can be attacked.

For Dúnhere this means the following. If you select him in the combat phase as an attacker, and he attacks alone, he can also attack enemies in the staging area. As mentioned on the card if he does so, he gets +1 attack. This does not mean that you cannot do other attacks.

See also this discussion.