Well, if you take one of the two : velocity or wavelength to be changing, change in the other will follow.
For the physical reason behind it, if I'm not wrong, I believe it is the average or effective speed of light that changes in a different optical medium; and between atoms, light still travels at 'c'. If you buy this argument, then to explain the change in velocity of light isn't so hard. The extra time light takes to cover the same distance in say, glass as in vacuum can be attributed to the time lag between the absorption and release of the photon of light by the medium's atoms. And there may be still a lot more going on inside than this.