Lithobraking (or litho for short) is a maneuver commonly used by players to add delta-v and reduce mass without staging equipment. As the name's etymology suggests, lithobraking requires a part or parts of a rocket to be destroyed by the surface of a celestial body to either reduce mass or provide an impulse to capture or slow down a spacecraft without having to consume fuel.
A successful lithobrake can be hard to execute due to the game's limited frame rate and the often high speed encounters where lithobraking is used. It is recommended to quicksave regularly as failed attempts are extremely common. To reduce the number of failed attempts, try lithobraking on the edge of a crater, summit of a mountain or crest of a hill as all of these areas reduce surface contact and therefore how much of the rocket can be destroyed.
A successful lithobrake on Ganymede.