Resting Heart Rate:

A measure of heat beats per minute when the body is completely at rest, such as in the morning right out of bed.
www.methodfitness.com/fitness_glossary_r.shtml

To determine your resting heart rate (RHR) is very easy. Find somewhere nice and quiet, lie down and relax. Position a watch or clock where you can clearly see it whilst lying down. After 20 minutes determine your resting pulse rate (beats/min). Use this value as your RHR.
If you have a heart rate monitor then put it on before you lie down. After the 20 minutes check the recordings and identify the lowest value achieved. Use this value as your RHR.
The heart is a muscle so with regular exercise it will become larger and become more efficient as a pump. As a result you will find your resting heart rate gets lower so you will need to check your RHR on a regular basis (e.g. Monthly).

Maximum Heart Rate:

Maximum Heart Rates are required in order to determine safe levels of training.
http://www.brianmac.co.uk/maxhr.htm

Heart Rate Training Zones:

Heart rate training zones are calculated by taking into consideration your Maximum Heart Rate (MHR) and your Resting Heart Rate (RHR). Within each training zone, subtle physiological effects take place to enhance your fitness.
http://www.brianmac.co.uk/hrm1.htm