The hydra reproduces by growing a new organism from the side of its tube

looking body. This is called

Budding.

Explanation:

In budding, the offspring develops as an outgrowth of the parent. The bud may form on an external or an internal surface of the parents. Internal buds here are formed in some sponges, and are released when the parents die.

External buds which occurs in hydra and coral polyps. These buds break off from the parent without causing any injury and lead an independent life.

It is well noted that in multicellular animals like in the hydra, the cells in the bud undergo differentiation to form the complex body of the organism.