Galieleo’s relativity stated that an observer who moves uniformly with constant speed in a straight line, that is, who moves with constant velocity, is called an inertial observer. The Galilean principle of relativity can be stated as follows: The mechanical laws of physics are the same for every inertial observer. In other words, by observing the outcome of mechanical experiements, one cannot distinguish a state of rest apart from a state of constant velocity.
By Galileo’s definition, two inertial observers can disagree on whether or not two separate events occurred at the same position in space. Since no mechanical experiment can distinguish a state of rest from one of uniform velocity, Galileo effectively abolished the universality of the notion of an ‘observer at rest.’
Information from Bruce Gordon’s lecture “Relativity Theory and the Nature of Time.”