Its often just turning a mana dork (think Dyad Arbor ) into something that ends the game
Casting Aetherize at four converted mana cost is very overkill, but with Cyclonic Rift, you can just pay the normal one-generic, one-blue cost to deal with the problem instead
It bears the Crew ability word - specifically Crew 3, requiring you to tap any number of creatures you control with total power of three or more in order for Cultivator's Caravan to become an Artifact Creature
Despite it being an uncounterable creature that you can cast at flash speed, one of the most common things to do with Hullbreaker Horror is cheating it into play with a card like Polymorph
For example, the text of Valakut Exploration specifically says: You may play that card for as long as it remains exiled. The word play indicates that you can play lands that you exile with this ability
Giving creatures the ability to attack or tap on the same turn they enter the battlefield under your control lets you quickly apply pressure to opponents through big stats, attack triggers, and powerful abilities the table would otherwise have a turn to respond to