This is because the colors in plants come from compounds called plant pigments, and these plant pigments often have slightly different structures when in acid (low pH) and when in base (high pH). As a result of the different structures of the pigment molecules, the colors are different.

The color of flower petals is determined by pigments in the fluids inside of the flower's veins (petals are modified leaves, and so have veins just as normal leaves). Under different chemical conditions, the pigment molecules might switch to a different chemical state, changing their color. pH is certainly one chemical condition, and I would imagine that they would change with temperature, concentration of salts, etc.

Different flower petals change color in different pH conditions for different reasons. It all depends on which pigments the flowers use to get their colors. In general, very small changes to a molecule (like a flower pigment) can cause it to change color, and different pH conditions can easily cause those changes. pH can change the electrical charge of a molecule, or it can change what the molecule can bind to. Both of these things can change how the molecule interacts with light, which means we see it as a different color. This same principle is how pH indicators work, by the way.