The colonyship is what you use to colonize other planets. They carry 100 colonists to the new planet to start a new colony. Colony ships are quite expensive and slow to move, it's a good idea to ensure the target star has been cleared of all resistence before sending in the colony ship. It's not one you can afford to lose.
Colony ships are single-use. Once a planet is colonized, the ship is destroyed.
The cyrogenics upgrade adds a cyrogenic module to the colonyship. By putting colonists to sleep while they travel, you can pack them in a whole lot tighter, which allows you to increase the capacity of the colonyship from 100 colonists to 400 colonists.
Note that if you colonize a planet with < 400 population congeniality, you will lose any colonists over the planet's congeniality.