An imaginary line around a circuit that provides the quickest lap time. When turning into a right-handed corner, the quickest line is to enter on the left side of the track, turn in and 'touch' the apex and ease back out to the left side of the track. Opposite for left-handers.
Not necessarily the shortes, but the fastest course around the track. When driving the racing line, the vehicle is taking the curves with the largest possible radius, allowing higher cornering speed which will also carry more speed along the straights.
This is the optimum line around a race circuit, therefore in theory it is the fastest way around a circuit. For a lone corner this is usually a wide entrance, followed by a defined ‘apex' which is near the middle of the corner on the inside, and a wide exit to allow all the power to be used. It is the straightest line through a corner.
The fastest way around the track, but not necessarily the shortest in terms of distance. This usually entails taking a wide radius around corners so cars can maintain higher average cornering speeds.
In motorsport, the racing line is the fastest path a vehicle can take through a specific corner, series of corners, or track. The racing line is generally characterized by creating the largest turning radius possible within the confines of the track. A simple example would be a 90 degree left turn.