It is a way to communicate with others using one's mind. Users can also read the minds of the ones they communicate with, similar to telepathic eavesdropping.
The ability to communicate telepathically does not seem to be hindered by time dilation, as Piccolo is able to talk to Goten and Trunks while they are in the Hyperbolic Time Chamber during the Fusion Saga, despite him being outside of it.
When Slug used it on Bulma, she seemed to become dazed and confused while he was searching her memories.
Mind reading notably has some difficulty being effectively used against people who have low intelligence. This is best demonstrated when Korin attempted to use his telepathy to read Maron's next moves in a Poker game, only to fail as "[Korin] has seen party balloons with more on their mind [than with Maron]."
King Kai is possibly one of the most famous users of this technique, as he is able to speak with people all across the universe and countless people at one time, something the Supreme Kais thought was impossible. It can be assumed that he taught it to Goku while he trained with him in Other World, as Goku uses this to stop Krillin from finishing Vegeta after their battle on Earth.
It was also used by Shin to read the mind of Piccolo while the two were facing each other at the 25th World Martial Arts Tournament.
During the Tournament of Power, Vermoud uses it to communicate with Jiren to attack Goku. Jerez uses it to communicate with Ribrianne and Roasie. Through his robot suit, Mule uses it to communicate through Paparoni's cane to instruct Team Universe 3 to attack Team Universe 7.
Pan used it to communicate with Goku underwater during their fight with Haze Shenron.
In the Super Dragon Ball Heroes anime, Hearts uses his ability to read hearts on Hit to find out who the strongest in all 12 universes is. Hit is shocked when Hearts correctly guesses that Jiren is the strongest, and questions if Hearts read his mind.
In Dragon Ball Z: The Return of Cooler, Cooler's surviving head used it to communicate with Goku and Vegeta after they were brought to him inside the Big Gete Star following their defeat by his Meta-Coolers. He speaks normally when assuming his battle form, however.
It is implied that Goku was using telepathy to communicate with the other Z-Fighters when planning to have them donate their energy to Goku to empower him enough to stop the Legendary Super Saiyan Broly in Dragon Ball Z: Broly - The Legendary Super Saiyan, as he was communicating with them despite being far away from them, and in one scene, Goku's voice is heard with an echo effect. Unlike other instances, however, the characters lips move during these instances.
Video Game Appearances
In Dragon Ball FighterZ, Piccolo uses it to read Bulma's mind from afar to learn about the situation while recovering aboard her ship being saved by Goku and Krillin. Krillin attributes his skill with the technique due to his fusion with Kami, stating that Kami was an old hat when it came to reading minds.