The muons (µ+ and µ-) are created in the cosmic radiation that constantly bombards the earth's atmosphere. The major part of this radiation consists of protons, which produce new particles (most often pi-mesons) in the collision with the molecules of the atmosphere. These particles decay into (among other things) muons. The muons also decay rapidly into other particles (e+, e- and neutrinos).
The life time of the muons is so short (about 2.2 micro seconds) that the muons created by the cosmic radiation at a high altitude (some tens of kilometres) should not have time to reach the surface of the earth before decaying. But muons can be detected at the surface of the earth in detectors called cloud chambers. This can be explained with time dilatation, which is a result of Einstien's special theory of relativity (1905).