Why does raising the surrounding pressure raise the vapor pressure of a liquid?
The answer lies in that the chemical potential of the liquid increases with pressure.

Quantitatively, the chemical potential changes with a change in pressure from $p_1$ to $p_2$ as follows: 
$$\Delta\mu(\textrm{l})=\int_{p_1}^{p_2}V_mdp$$

A qualitative explanation is possible by linking the change in pressure to the concept of chemical potential. The chemical potential difference is the amount of non-pV work (the "chemical" work) which the system can perform. In essence, increasing the pressure means more of the liquid has the potential to transfer into the gas state (the chemical work in question).   You might visualize the transferred molecules as being "squeezed out" of the liquid by the increasing pressure applied by their neighbours.