Haste is a special ability in Magic the Gathering Tactics.
When a figure with haste is summoned, it's inserted as the next figure on the initiative bar. Effectively going next in the turn order.
A figure with haste can change the board dynamic very quickly.
Opponents get no time to react to the new threat on the board and effectively can't cast instants against it, until after its first turn.
When combined with defensive abilities, such as first strike, a creature with haste can make a surprise appearance and a sustaining impression.
The traditional Magic card game and the tactics game give haste almost the same application.
Haste is stronger in Magic the Gathering Tactics because creatures can attack other creatures, instead of opponent controlled blocking.