Aerobraking
Aerobraking is a technique to lose velocity after reaching a celestial body.
Usually when the craft enters the sphere of influence of a celestial body, the relative speed to it will be much too high to enter an orbit, unless burning retrograde and expending a lot of fuel. In order to save the fuel, the craft can either perform a gravity assist or perform an aerobraking maneuver.
To perform an aerobrake, the trajectory of a craft has to be altered to pass through the atmosphere of a celestial body. The atmospheric drag will slow the craft down enough to reach an eccentric orbit around it. After the apoapsis is lowered to the wanted altitude, it is necessary to raise the periapsis outside the atmosphere to prevent additional aerobraking maneuvers.
Aerobraking is a dangerous maneuver. When the craft dips too deep into the atmosphere, it will lose too much speed and risk crashing. When it doesn't dip deep enough, it might not lose enough speed to enter an orbit. Usually it is better to be careful, because even when the orbit turns out to keep it just barely in the SoI of the planet, the orbit allows it to perform additional aerobreaks to slow it down more. In the current version (0.18.4) flying through an atmosphere at high velocity is unlikely to damage a craft (except for extended solar arrays), but it was already announced that later versions will implement reentry heat. This factor could make aerobraking even more dangerous.
For the ideal height for an aerobrake maneuver, consult the article about the planet. The following planets and moons have an atmosphere which allows aerobraking:
