The supernova explosion of a star is sometimes symmetrical and sometimes not. When the explosion is not symmetrical some of the energy of the explosion gives the resulting neutron star a kick sideways. The results of that can be spectacular.
The Guitar Nebula is indeed a spectacular example of what can happen when a neutron star gets a sideways kick:
Back in 1992 a group of researchers from Cornell University used the Hale Telescope at Palomar Observatory to discover a unique nebula associated with a high-velocity spinning neutron star (also called pulsar) known as PSR 2224 + 65. This pulsar is flying through a gas cloud and producing shock wave in the gas very much like the wake of a boat moving through water. The result is the Guitar Nebula.
The pulsar is flying through a gas cloud at an amazing speed of about 800 km/s (1.8 million miles per hour!), fast enough that it will eventually escape the Milky Way galaxy. It is also fast enough that it is possible to watch the neutron star move in just a few years time.
Given the Guitar Nebula's distance (about 6,500 light years away, in the constellation of Cepheus) and apparent size in the sky (1 arc minute) astronomers estimate that the neutron star has been traveling for 300 years.