Gears on bicycles have been around for over a hundred years and every bike has some sort of gear system even if it is a single gear. Mathematically gear ratios are obtained by taking the number of teeth in the rear sproket and dividing it into the number of teeth in the front sprocket and mutiplying it by the diameter of your wheel. This will give you the distance you would travel on level ground without coasting.
Low gears make it easier to ride up steep hills and high gears make it faster going downhill. Racers make a constant number of revolutions with the crank, pedals, and adjust the bicycle’s gears to accomodate the terrain which s/he is travelling. New racing and casual bicycles come with gearing as high as eight chainrings in the rear sprocket and up to three on the front sprocket giving you a total of up to twenty four possible gears to utilize during your ride.
Most casual riders will use these gears in a limited way hardly getting off the middle sprocket in the front. One should experiment with his/her gearing to get comfortable with how useful and powerful the bike can be when it’s used to its capacity.