Heating services technicians won't hesitate to tell you: household thermostats have evolved quite a bit from the simple round dials of 20 years ago. Their main job, however, is the same: to keep your home environment comfortable by allowing you to set the temperature that your heater comes on. Essentially, the thermostat is a switch that, at a certain temperature, turns on and completes a circuit, activating your heater. (If you have heater and AC through the same thermostat, it's two switches, set to activate at two different temperatures.)
Generally speaking, the same switch that activates your heater will also turn on the system fan, so that the hot air makes it around your home. Naturally, if you have radiant, baseboard, or other non-ductwork heating methods, this rule doesn't apply.
If you have electric baseboard heating, or any other heating that requires a high-voltage thermostat, do not ever attempt to replace the thermostat yourself. In addition to all of the other problems below with DIY thermostat repair, the voltage running through those puppies will actually kill you. Don't mess!
Not all thermostats work with all heating systems. Thermostats come in 2-wire, 5-wire, 8-wire, and a variety of other less common configurations. Trying to use a more complex thermostat for a less complex system is a waste of money, and trying to use a simple thermostat for a more complex system can cause vast damage to the system in question.
A non-programmable thermostat sets the temperature via a physical device; usually a knob. Once you set it, it doesn't change until you set it again by hand. Compare that to a programmable type, which allows you to set various factors that will change the temperature in your home. Depending on the complexity of the system, it can be as simple as a clock that turns the heat on in the morning and off at night, or as intricate as multiple zones in your home, each with motion sensors that tell the system how many people are active in the area, altering the temperature accordingly on the fly. Suffice to say, programmable thermostats require input from a variety of devices, and dealing with the wiring can be quite complex.
In many cases, it might be advisable for a landlord or building rep to prevent others from tampering with the thermostat programs. If you don't have the keypad code, you won't be able to set some (or possibly even any) elements of the keypad's function. Some models also offer setpoint limiting, allowing you to, for example, prevent someone from putting the 'activate heater' temperature anywhere above 69 degrees. If you miswire a thermostat with a keypad lockout, you can end up inadvertently locking yourself out until you take it apart and reassemble it.
Hopefully by now you get the idea -- compared to the thermostats of 20 years ago, today's are almost miniature computers, and if you don't know what you're doing, you'll fry the thing and end up down the cost of the thermostat as well as the cost of hiring a heating services expert to install the thing properly. Don't let that be you -- just hire the right team the first time.