There are many ways you can kill lice. You can suffocate them, poison them, or dry them out. You can also starve them if you get them away from their food source - your head - long enough (they'll die within 24-48 hours).
A louse gets air into its respiratory system through tiny openings (called spiracles) in its body. If you can sufficiently coat those spiracles with a viscous substance (e.g. mayonnaise), you can actually cut off the louse's breathing. It can work, but lathering your head with a household product and waiting for it to suffocate the lice can be a messy, time-consuming endeavor. There are also synthetic products designed to do this. Learn more about suffocation products and their effectiveness at killing nits and lice.
There is a fancy word out there called "pediculicide." It means pesticide (or insecticide) used for killing lice. If you buy over-the-counter lice shampoos (or similar lice products) that don't tout themselves as "chemical-free," they most likely will contain a pediculicide as an active ingredient. The pesticide in the shampoo (and stronger prescription-based products) will poison a certain percentage of the head lice upon application. Learn more about lice pesticides and lice resistance to pesticides.
Desiccation is a fancy term for "drying most of the moisture out." Like you, lice can't survive without enough moisture in their systems. You can dry lice out with heat or air, but to do it effectively you have to get the right temperature and the right airflow close to the scalp, where the lice and eggs are. This is how the professional AirAllé™ device kills lice and 99.2 percent of lice eggs. Learn more about AirAllé.
Keep in mind, however, that killing lice and killing lice eggs are not the same thing. The eggs are harder to kill. Even if you kill all the lice in your hair, you're going to get them again a week or so later if you don't kill or remove the eggs too (and lice eggs can be very difficult and time-consuming to completely remove).
So now that you know how you can kill lice, you'll probably want to learn which lice treatment is best.