The Pulsar is a device that shoots electromagnetic pulses that can heal sick or injured animals. These pulses can also calm down aggressive animals (at least temporarily), and prevent them from attempting to attack the player. However, some creatures can shake off the effects of the Pulsar very quickly, and should instead simply be avoided (when possible).
Near the beginning of Endless Ocean: Blue World's main plot, Oceana goes to Deep Hole to attempt to retrieve a lost pendant that she dropped there many years ago. Jean-Eric tried to warn her against it, because of the dangerous Tiger Sharks that occasionally go to hunt there, but Oceana refuses to listen, and goes anyway.
True to Jean-Eric's warnings, Oceana is almost attacked by an aggressive Tiger Shark. Before the player goes to rescue Oceana, Jean-Eric gives the player the Pulsar. He explains that its original purpose is to heal animals, but it can also be used to calm down agitated creatures, and that the player should go calm down the Tiger Shark that's trying to go after Oceana.
The player uses the Pulsar on the Tiger Shark, and it swims off. Oceana finds her pendant, and they both return to the boat. After receiving a chastising from her grandfather, Oceana promises to not pull any more dangerous stunts like that.
After that incident, the player has access to the Pulsar from their inventory for the rest of the game. The pulsar can later be upgraded to have more pulses. Additional pulses can be bought from Nancy.