A charged particle with charge $q$ is moving with a uniform velocity $v$. So it has an electric and a magnetic field associated with it. Now if I, the observer, start running parallel to the charge with uniform velocity $v$, then, the charged particle appears to be static from my reference frame and hence I see that its associated magnetic field has, all on a sudden, vanished. But a stationary observer still finds that the charged particle has an associated magnetic field.