I am a beginner myself; so correct me where I am wrong. This post and its followups are based on what I have understood reading articles and watching videos on the net.
Key-Light is the main light for the subject; its job is to create the proper shadows. This can be hard or soft; depending what kind of shot one want. In Classic Three-Light setup it’s usually placed at a 30 to 60 degree angle horizontally. Key-Light can be placed low or high; for portraits it’s usually at 30 degree angle high with an intention that nose shadow is not casted on lips. For portraits keeping it low is not considered good as it gives horror movie like effect. The strength and color of the Key-Light determines the overall lighting design. The brightness of the Key-Light is not considered important, as you can always move the Key-Light near or far. For indoors; flashgun or specialized light is used, and for outdoors; the sun often is used as Key-Light.
Fill-Light keeps the details in the shadows; it also falls on the subject and usually from a side angle relative to the key and is often placed at a lower position than the key at the level of subject’s face. Its job is to illuminate the shaded areas. Its kept softer and less bright comparing to Key-Light.
Back-Light is always behind the subject and kept usually at 120 to 170 degree. It’s usually placed high with angled down. If its narrow and is hitting hair its called Hair Light, and if it spreads more widely and falling on one or both shoulder then it’s called Rim-Light. Rim-Light separates the subject from the background highlighting contours.
Image is from Wikipedia
If the subject is near to some background object on which Key-Light is causing subject’s shadow and one wants to remove this shadow, the fourth light Background-Light is introduced (making it Four-Light Setup) and its objective is to remove the subject’s shadow and/or highlight the background elements. The Background-Light is usually kept low to the ground.
Image is from Wikipedia
Take a look at Three-point lighting - Wikipedia, the free encyclopedia; there is an animation that shows the three-light setup!