hydrophobic effect
Think of oil droplets coming together in a glass of water. The oil and water do not actually push each other away; instead, water molecules prefer the company of other water molecules, so they squeeze the greasy bits together to keep the most water-water contacts. That self-organizing of water is the hydrophobic effect, and it is one of the strongest forces driving a drug into the greasy parts of a binding pocket.
The driving force is largely about entropy. Water touching a nonpolar surface has to arrange itself into a more ordered, cage-like shell because it cannot hydrogen-bond to the greasy surface. When two nonpolar surfaces come together, that ordered water is released back into the bulk, gaining freedom and disorder. The resulting entropy increase makes the burial of hydrophobic groups thermodynamically favorable.
Medicinal chemists exploit this constantly: adding a well-placed lipophilic group that buries snugly against a hydrophobic patch of the target can boost affinity substantially. The danger is overdoing it. Too much lipophilicity worsens solubility, raises off-target binding and metabolic liability, so the gain in potency must be weighed against the cost in drug-like properties.
Because it is mostly entropic, the hydrophobic effect is unusual: it can actually strengthen as temperature rises over a moderate range, unlike most enthalpy-driven interactions.