A bit oversimplified: when one tightens a violin string 1) in tuning the instrument or 2) by depressing ("stopping") a string while playing, one effectively shortens the string. To clarify, in the case of stopping a string by fingertip, one is effectively removing a part of the string closest to the pegs; in the case of tuning, one removes a part of the string from the fingerboard by winding that part up on a peg. All of this shortening causes additional tension in the string. Increased tension increases the frequency produced when the string is bowed or plucked, causing a higher pitch. Loose strings vibrate more slowly and producer lower pitches and the opposite is true.
Thanks for the question!