The 'force' that sequesters nonpolar sidechains into the hydrophobic core of a protein.
The adage - 'oil and water don't mix' is a manifestation of the hydrophobic effect. Nonpolar molecules in an aqueous environment are likely self-associate rather than remain solvated. Hence, you can't dissolve oil (or hexane) in water. The force that drives the oil molecules to associated and separate from the water isn't really an energetic force in the regular sense. Instead, it is an entropic effect. Entropy can be thought of as the state of disorder of a system. Systems tend to greater entropy, unless energy is put into the system to impose order on it. When water meets a nonpolar molecule, it forms highly ordered clathrates similar to those found in ice. This is entropically unfavorable. Additionally, because oil is nonpolar, there is no energetic benefit to water associating. Hence, there is both an entropic penalty and no energetic gain. However, there is a much smaller penalty for two oil molecules to associate, and some energetic gain from dispersion. As a result, oil association occurs more often than oil solvation.
In a protein, there are 'oily' residues, those which are nonpolar such as leucine, phenylalanine, valine, etc. These, when surrounded by water, form the same clathrates. As a result, nonpolar (also called hydrophobic) residues tend to cluster inside of a protein, protected from the water. On the outside are left the polar and charged residues, which form energetically favorable interactions with the water.
The term hydrophobic collapse refers to the quick association of hydrophobic residues in the initial stages of protein folding. It is believed after hydrophobic collapse that the nonpolar residues dance around each other in the molten globule state until they find the optimal packing arrangement and the protein settles into the native state.
For other protein stabilization forces, see: