How does the structure of the cell membrane lead to its selective permeability?

What are you taking a test or something? Here goes:

The cell membrane is a phospholipid bilayer with a hydrophilic exterior and a hyrdophobic exterior. Because of the thick hydrophobic interior, charged particles (e.g. ions) cannot cross without assistance, and must go through specialized channels. Small uncharged molecules like water can pass in and out easily. This allows the cell to control the flow of ions and, with them, water. I'm sure wikipedia has a whole blurb on it...

the cell membrane is made up of the phospholipid bilayer which has many proteins scattered on it (hence the term 'fluid mosaic').
There may a few different kinds of proteins, such as channel proteins and carrier proteins. These proteins have specific conformation which can bind to specific molecules only, allowing them to enter the cell. Thus, only molecules which can bind to the carrier / channel proteins can enter into the cell.
Water moves into the cell by osmosis, and small uncharged particles can pass through the bilayer into the cell. However, large polar particles only can pass through the proteins because the bilayer is hydrophobic.