This term is usually reserved for the 5th and 6th centuries. Re-enactors who re-create the next period of history - 7th to 11th centuries - often refer to this as Early medieval. The 12th to 14th are High medieval.
A medieval reenactment is a form of historical reenactment that focuses on re-enacting European history in the period from the fall of Rome to about the end of the 15th century. The 2nd is the Middle Ages.
The principal aim of this sort of reenactment is to re-create historical battles or methods of combat. The variations range from the training of historical dueling practices (usually with an appropriate period sword.
It is usual to fight using more restricted target areas than in a real fight and with less speed and force, although some systems try to get as close to real combat as possible. Many societies try to reenact actual battles.
In Sweden there are many different "medieval markets". The largest is the one in Gotland. In Szeklerland, Transylvania are many Hun, szekler knight, early Hungarian and hussar reenactment groups and camps.