This effect keyword was introduced in the Call of the Crystals set.
Haste is a keyword passive ability (written in bold in the effect area of the card).

Definition:

Haste applies specifically to summoned allies.
An ally with haste can attack or use its activated abilities on the same turn it is summoned. Normally, when an ally is summoned, it enters play exhausted, meaning it cannot attack or use its abilities until it is readied, or until the following turn.
Some allies have haste as one of their own abilities, other times they can be given haste by card effects.

Immediate Action:

The main advantage of haste is that it allows the ally to have an immediate impact on the turn by attacking or using abilities as soon as it enters play. This can be crucial in situations where you need to finish off a weakened opposing ally, or for other purposes the haste ally may have.

Some Statistics:

• Human faction has 6 allies with haste, Neutral faction has 3, and Shadow faction has 2.
• Note: Only the Priest and Elemental classes have no specific card that possesses or grants haste.
• Note: When the trap Camouflaged Foe's ability is triggered, it enters the ally row as a readied ally.

The cards related to haste are