This work tries to elicit the "meanings" that undergraduate physics students attach to the term "relativity". The domain of investigation is restricted to Galilean relativity of Newtonian mechanics. Our methodology is primarily qualitative: we first obtain students' responses through a questionnaire, follow it up by a 3h teaching session and tutorial on the topic, and administer another questionnaire probing much the same notions as the first. After preliminary analysis, we interview some of the students for clarification and confirmation of our interpretation. The focus of our study is on the "meanings" that students ascribe to the principle of relativity (RP), rather than investigating the whole range of technical concepts of this subject. Three meanings (apparently separate but in fact entirely equivalent) of the RP are identified, namely (i) the inadmissibility of the notion of "a frame at absolute rest", (ii) the inability to determine the "velocity of a frame" from measurements with respect to the frame itself and (iii) the absence of the "velocity of frame" term in the pseudo forces for a non-inertial frame. The results indicate that most students trivialize the RP through its "kinematic" interpretation (as explained in the text) thus rendering it empty of its dynamical content, invoke causal-mechanistic explanations than use the constraining power of the RP and are unable to see that the three meanings of the RP indicated above are simply different ways of saying the same thing. (Contains 5 footnotes.)