This is usually a power rating... basically the backbone of the rod... what its lifting power is for want of a better explaination...
Light ratings are gonna mean the rod has light lifting power, usually rated in a vertical pull.... It may handle the same line as a heavy power rod, but in a vertical lift, the heavy power rod will be able to handle a much heavier load...
If you pick a rod up, and compare a light power to a heavy power, you can feel the difference, even if they are rated for the same line class... the light power will probably be more sensitive, but the heavy is gonna have more backbone...
Then you can look at actions... slow, medium, and fast.. Personally I prefer fast action rods.... Better perfromance in the wind, more accuracy and just feel better... I hate sloppy sticks...