From Latin medium aevum: middle age.

It entered into English (ie anglicized) in the early 19th century, and the Latin spelling tells us why sometimes you'll see the alternate English spelling mediaeval. Up until then a lot of history-writing was in Latin language where the concept of 'medium aevum' developed over the previous centuries. The first appearance of the idea of middle ages shows up in the late 15th century and early 16th century, and by the turn of the 18th century the idea is firmly cemented in the western historiographical model as the 'middle' of 'antiquity-middle ages-modern'.