For me, medeival means knights in shining armor, damsels in distress, bards plucking a grand ol' tune around a camp fire and of course massive armies crashing headlong into one another on the field of battle. Swords, shields, power and poverty can all describe this interesting field. Add to it a bit of fantasy elements and you've got a great genre to play and read.
To me, Medieval parallels with the period of the Dark Ages, widespread feudalism, and widespread superstition. It is a time where you either ruled most of the land, were practically a slave to those who ruled, or were a rouge. If you were playing a game, Medieval would probably turn superstitions into magic, and science into alchemy. Medieval equals a sucking, but always adventuresome life.
Medieval to me means a time where courage was rewarded and intelligence was rare but powerful. Where battles where fought with honor and bravery, with real weapons, face to face, sword to sword by skilled soldiers and brave warriors. Where heros were loved for their selfless and brave deeds against those who were ruthless, greedy and murderous. A time of hard work and appreciation for the real necessities of life.