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 enslaved by the spell known as the geas, 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 both, prerevisionist way and the creation of a faux entity based on the concept of that creature, which is pulled from the Æther. 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-Dûl to Jodah. Though Jodah is not in fact summoned, as Lim-Dûl 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 similar to this, but based on the concept of a specific individual and not simply off of a group. It is also described in The Eternal Ice.