We all know about the Time And Relative Dimension(s) In Space acronym explanation of this name. Yes. But part of the reason why 'Tardis' sounds sort-of right as the name of a time machine is its 'tard' element: a temporal concept (from the Latin tardo, 'to make slow, to hinder,delay, retard, impede, prevent') that echoes in the English 'tardy' and the French 'tard'. We might think the machine 'retards' itself, temporarily speaking, to go back in time; or holds itself steady and 'retards' a bubble of spacetime around it to go forward.
Maybe the actual name of the machine should be the future-perfect ('you will have tarded'): tardaveris. Maybe it is, and tardis is only a contraction. But, then, why the second-person singular? Ah the mysteries of Who.