Summon

Summoning is the process by which a magic-user calls forth, or 'summons' a creature to do their bidding.

Prerevisionist

Summoning in prerevisionist materials was the literal movement of a being to the presence and control of the mage or planeswalker summoning it. Some summoned creatures agreed to be servants of the spellcaster, while others were more or less treated as slaves to be used in magical combat. If the wizard doing the summoning was victorious, the summoned creatures were usually returned to their places of origin; but if the wizard failed, the surviving summoned creatures would be stranded where they were summoned to.

Revisionist

The modern idea of summoning involves not the actual movement of a creature, but the creation of a faux entity based on the concept of that creature. These summoned creatures have no will of their own, and vanish when no longer needed. This concept is described in The Eternal Ice by Lim Dul to Jodah. Though Jodah is not in fact summoned, as Lim Dul suggests, the explanation is still valid and continues to be the best flavor related description of the summoning process.

The summoning of unique, Legendary individuals is a take off on this, but based on the concept of a specific individual and not simply off of a group.