This pronoun is the objective case of the equally archaic pronoun thou. Despite its archaic standing, thee has an important place in the vernacular; at traditional wedding ceremonies the bride and groom say to each other With this ring, I thee wed.

At the turn of the seventeenth century, thee and thou were at an all-time high in written usage. However, by the 1620s, you had overtaken these now old-fashioned-sounding words.
In English there used to be both plural and singular forms of you. Thou (nominative) and thee (objective) were used to refer to an individual, while ye (nominative) and you (objective) were used to refer to a group of people or as a polite address. The nominative plural form ye gradually transitioned into you, making ye uncommon by the seventeenth century. The singular forms took on informal connotations, and fell out of usage in favor of the polite you. By the mid 1600s, you was used in the context that thee, thou, and ye had historically been favored.