What makes a cell membrane waterproof?
A cellular membrane cannot really be considered "waterproof".
A cellular membrane is composed of a phospholipid bilayer (for reference search fluid mosaic model). The bilayer forms in aqueous environments because of the amphipathic properties of phospholipids, where the phosphate head is hydrophilic and the fatty acid tails are hydrophobic.
The bilayer automatically self assembles as the fatty acids will face each other and the phosphate heads would be facing out.
The cellular membrane is considered selectively permeable, meaning while some small molecules can move freely in and out of the membrane other molecules may need to pass through the membrane through facilitated transport.
Generally, cell membranes allow water to move freely in and out of it, thus it doesn't really keep water out of the cell as the word "waterproof" would suggest.
The movement of water through a semipermeable membrane is called osmosis and this free moving of water is what keeps the balance between the outside and inside of the cell. It is part of the homeostasis of the cell.
Osmosis will occur until the water potential on both sides of the membrane are the same, thus the cell can shrivel in hypertonic solutions or burst in hypotonic solutions.
Allott, Andrew, and David Mindorff. Biology: Oxford IB Diploma Programme. Oxford: Oxford UP, 2014. Print.