I find this might be a little easier to grasp, but basically says the same things mentioned in the above, with a little added explanation. 🙂
If you are looking at a solute dissolving in a solvent, the nearby solvent molecules form the solvation layer around the solute.
From an enthalpy standpoint, even things like hydrocarbons are going to have more stability in an aqueous solution as opposed to organic solutions (ΔH < 0). Conversely, if an amino acid with a hydrophobic R group is dropped in an aqueous solution, the water molecules in the solvation layer can't hydrogen bond with the side chain. This inability to hydrogen bond forces the water molecules nearby to rearrange themselves into specific patterns to maximize hydrogen bonding. Therefore you have a negative change in entropy , or ΔS. Because you are seeing negative change in entropy (decrease in disorder = increase in order), it's unfavorable. So the overall process is going to be nonspontaneous (ΔG > 0).
However, if there's a hydrophilic residue on the protein's exterior, that will allow these nearby water molecules more freedom in their positioning, which means their entropy will increase (ΔS > 0), and make the overall solvation process spontaneous (ΔG < 0). So a protein is able to achieve maximum stability by pushing hydrophobic groups to the interior of a protein, and keeping hydrophilic groups on the outside.