The temperature of a gas is a measure of the average kinetic energy that the particles have. For a complete discussion of this idea and the difference between temperature and heat, go here.
For most of the unit, we just need to understand that the hotter a gas is, the faster the particles move.
If you want to understand Graham's Law, you will need to know a little more. Specifically, you need to know the formula for kinetic energy.
KE = ½ m v 2
In this equation, the m stands for mass and the v is the velocity of the particle. This formula means that the when the velocity doubles, the KE (and therefore the T) quadruples. Or, in a more useful form, if the temperature is quadrupled the molecules are moving twice as fast.
Temperature is generally measured in degrees Celsius (also called degrees centigrade), symbolized oC. This is the unit that most thermometers found in science classrooms and lab measure. However, we cannot use oC in mathematical calculations. For that reason we also use the kelvin scale, measured in kelvins, K. (Note: the Kelvin scale does NOT use a degree symbol.)
Converting between oC and K is done according to the equation:
K = oC + 273.15 or oC = K -273.15
You can visualize this by imagining a thermometer that records both temperature scales as seen below. Absolute zero (on the diagram) will be discussed later in the unit.