An analog temperature sensor is pretty easy to explain, its a chip that tells you what the ambient temperature is!
These sensors use a solid-state technique to determine the temperature. That is to say, they don't use mercury (like old thermometers), bimetalic strips (like in some home thermometers or stoves), nor do they use thermistors (temperature sensitive resistors). Instead, they use the fact as temperature increases, the voltage across a diode increases at a known rate. (Technically, this is actually the voltage drop between the base and emitter - the Vbe - of a transistor.) By precisely amplifying the voltage change, it is easy to generate an analog signal that is directly proportional to temperature. There have been some improvements on the technique but, essentially that is how temperature is measured.
Because these sensors have no moving parts, they are precise, never wear out, don't need calibration, work under many environmental conditions, and are consistant between sensors and readings. Moreover they are very inexpensive and quite easy to use.
TMP36 is a wide range, low power temperature sensor outputs an analog voltage that is proportional to the ambient temperature. To use, connect pin 1 (left) to power (between 2.7 and 5.5V), pin 3 (right) to ground, and pin 2 to analog in on your microcontroller. The voltage out is 0V at -50°C and 1.75V at 125°C. You can easily calculate the temperature from the voltage in millivolts: Temp °C = 100*(reading in V) - 50