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The hydrophobic effect is the solvent-mediated tendency of nonpolar regions to associate in water. Exposing a hydrocarbon region changes how surrounding water molecules can arrange and interact; reducing that exposure can lower the total free energy. Both water and lipids enter the accounting. The effect is not an additional covalent bond between chains. See IUPAC Gold Book: hydrophobic interaction.

At fixed temperature and pressure, compare two candidate organizations by the change in Gibbs free energy, $\Delta G=\Delta H-T\Delta S$, where $H$ is enthalpy, $T$ is absolute temperature, and $S$ is entropy. An organization with lower $G$ is favored in this comparison. Reducing exposed hydrocarbon area is one contribution; changes in chain packing and the entropy of the lipids also matter. This explains why hydrophobicity alone cannot predict every aggregate shape. See 16.4 Free Energy.

Hydrophobicity describes unfavorable mixing with water, as illustrated by long hydrocarbon regions. The hydrophobic regions of membrane-forming phospholipids face the interior of a lipid bilayer. This organization is explained by the hydrophobic effect, rather than by imagining that chains actively repel water. See IUPAC Gold Book: hydrophobic interaction.

The protein tertiary structure is the overall spatial arrangement of one polypeptide chain. It includes how its protein secondary structures and intervening regions fit together. For example, the schematic under protein places positions 4 and 9 near each other despite their separation in protein primary structure. Such cooperation can help construct an active site; sequence distance and spatial separation answer different questions. Hydrophobicity, backbone hydrogen bonds and other interactions help stabilize folds, and some proteins additionally contain protein disulfide bonds. See Cooper: tertiary structure and interactions between chain regions.