Dimmers are electrical devices found in homes that adjust the light incrementally from near dark to bright by turning a knob or moving a switch. Dimming a light bulb not only adjusts the light output but also the heat, so dimmers are often used in reptile keeping in order to attain a precise temperature. You can purchase a dimmer at a hardware store or home improvement store and it plugs directly into the wall or timer, and then your lamp plugs into the dimmer.
AC wattage is an alternating current that goes from positive (on) to negative (off) 120 times a second. When the current is interrupted by a dimmer, the light bulb switches on and off rapidly, many times a second, and the actual intervals between the light being switched on and off influence how dim the bulb is. The dimmer has a variable resistor inside that increases the resistance to the current when in the dim position, and decreases the resistance while not dimmed. Greater resistance means it takes a longer length of time to turn the current back on, and the bulb would have a dimmed appearance. Less resistance means the current is switched back on more quickly, having less interrupted current time and making the light brighter. If you are using a dimmer and it makes a buzzing sound when the light is dimmed, it is one of a cheap design. The choppy current flowing through a cheap dimmer changes the magnetic field inside of the light bulb suddenly, vibrating the filament and causing a buzz.
So what does this information mean to you and your bulbs or light fixtures? Always check the package instructions or call the manufacturer and ask when you are not sure if your specific bulb can be used with a dimmer. Dimmers can shorten the life span of some bulbs, and are not for use with many compact fluorescent bulbs. Read all instructions for heat mats, pads, ceramic heat emitters and heat tape to make sure they are safe for use with a dimmer. Do not use a dimmer with a UVB or mercury vapor bulb as MVBs are self-ballasted and have two types of filaments in the bulb, both incandescent and UVB. To ensure accurate temperatures, always check the temperature with an accurate sensor/probe thermometer or temp gun after adjusting the dimmer.
Thermostats are controls that keep the temperature of a device constant by either turning the device on and off, or pulsing the current at a lower or higher speed. Your thermostat choice will depend on the device you need to control. The on/off type of thermostat is best for your heat/light bulbs and the pulse thermostats work best with heat mats.
The below website has a more comprehensive explanation of the thermostats sold for reptile use and is an excellent beginner's guide.