In my book it states each water molecule can hydrogen bond to 4 other water molecules. However, it does not state why this is? Why is it 4 molecules and not 3? Is this related to the electron structure of water?
Look at the water molecule structure:
Each hydrogen bound to the oxygen participates in the sigma bond with their single electron. The oxygen remains with two unshared pairs of electrons, thus, a remarkable dipolar moment is created and there's an heterogenous distribution of the electronic density in the molecule in this particular atom. In contrast, the hydrogens are stripped of electronic density in the covalent bond. When another water molecule approaches, the highly negative charges of its oxygen will undoubtedly have an attraction with each hydrogen; the sharing of one of these lone pairs with one of the hydrogens will cause what he know as hydrogen bonding. This far, we have two molecules stuck to the hydrogens.
Moving back to our original water molecule, we still have the oxygen with two lone pairs. In a similar fashion, each pair can interact with another hydrogen, therefore, we have our four adjacent molecules, as the following picture depicts:
In a discrete water molecule, there are two hydrogen atoms and one oxygen atom. Two molecules of water can form a hydrogen bond between them; the simplest case, when only two molecules are present, is called the water dimer and is often used as a model system. When more molecules are present, as is the case with liquid water, more bonds are possible because the oxygen of one water molecule has two lone pairs of electrons, each of which can form a hydrogen bond with a hydrogen on another water molecule. This can repeat such that every water molecule is H-bonded with up to four other molecules, as shown in the figure (two through its two lone pairs, and two through its two hydrogen atoms).
This is from the wikipedia article on hydrogen bonds. Hydrogen Bond
This explains the phenomenon with simplicity.