Dolphins jump for a number of different reasons.

 

Sometimes they jump out of the water out of simple playfulness.

 

Dolphins communicate through their movement as well as the sounds they make and jumping is one way to do that.

 

It can be a way of showing-off their agility or strength to other dolphins.

 

Leaping from the water may help dolphins glimpse the world above water, either to see what the weather is, or to identify potential threats.

 

Why do dolphins chase alongside the bows of ships? The bow wave helps dolphins go faster with less energy, so if they're travelling in the same direction, it's like hitching a lift. They may well just do it for fun though.