You carry a knife or sharp tool with you on a dive to make sure you have a practical tool at hand for safety and convenience. Besides the obvious cutting, you can use a dive knife to measure, pry, saw and pound whilst always being mindful not to harm aquatic life. You must remember, you dive knife is not a weapon! In some areas, local law prohibits or regulates the use of dive knives, so be careful that you are aware of local law and respect regulations on the length of the blade etc.
What makes them different from other knives, such as your standard kitchen knife, is that the metal used to make them, the design of the blade, the handle and how you attach it; read more on this in the selecting the right knife for you section.
You will never need a knife with a blade longer than about 4 inches, this length is more than capable for cutting yourself free from any fishing line or rope you may become entangled in. Unless you really need a big knife for activities like spearfishing, keep it small. This will not only be easier to carry on your person during a dive, but will also be suitable for most areas with knife regulations mentioned earlier.