Answer:
Firstly, Osmosis is the diffusion of water across a differentially permeable membrane due to concentration differences. That is to say, water (H20) goes from a higher concentration to a lower concentration, or from outside the cell (higher concentration), to inside the cell (lower concentration).
Secondly, water passively moves through a membrane channel protein now called an aquaporin, which is why water can cross a membrane more quickly than expected. This is a newer finding, but allow me to elaborate. The plasma membrane of animal cells is composed of a phospholipid bilayer in which proteins are embedded (integral proteins) or also occur on the cytoplasmic side (peripheral proteins). And the hydrophobic tails that make up the inside of the membrane, which you stated are "water-fearing." The aquaporin, as I stated previously is a channel protein. Channel proteins allow substances to simply move across the membrane freely.
This might sound confusing so here is a picture to illustrate what I mean:
The channel protein is the red object.
The membrane itself is depicted by the purple spheres.
Source:
Mader, Sylvia S.
Biology / Sylvia S. Mader. -- 10th ed.
