Combat is one of the most important parts of Guild Wars.
Battle alert pose
Characters assume a battle alert pose after attacking, taking damage, when an enemy begins to use a skill against the character, or when the character uses a skill with an activation time. The character returns to the idle pose after approximately 15 seconds of neither attacking nor taking damage.
"In combat" is while the character is attacking. When an allied NPC is attacking, they will refuse to start a conversation or continue one, but instead yell out phrases telling you to stop talking and start fighting, or indicating that they are busy.
Having "fought recently" means the character has been "in combat" within the last 15 seconds (approximately). Note that being attacked does not constitute having fought recently. The only visual indicator of having fought recently is the battle alert pose, which may be caused by other sources too (for example, taking damage).