There are single speed bike (1 gear) 3-speed bike (3 gears) 7-speed bike (7 gears) 21-speed bike (21 gears).
Fewer gears the bike has, less maintenance you have to perform on your bike. More gears your bike has the more maintenance you have to perform on your bike to keep her performing well.
The single-speed bike is best for flat ground/terrain. Like when you go ride at the beach on the strand or around your city where its relatively flat that doesn't have much incline. It will go up a good amount of hills but it will be much difficult to do with just a single speed. You are also limited to 1 speed which once you max out your speed you won't have another gear to grab and go faster.
The 3-speed bike is kind of like a single-speed bike. The 3-speed bike is good for flat ground and a little incline nothing big just mellow hills. 3-speed does have 3 gears but it doesn't work real good with big hills. Low gear on the 3-speed bike helps you pedal a lot easier but it's not a super low gear like the 7 and the 21 speed will offer you.
The 7-speed bike is made for flat ground terrain and you can conquer good amount of incline. The 7-speed bike is great all-around bike. It has low enough gear to go up a pretty steep incline and also has a high gear to go pretty fast. It's perfect for everyday riding around town or at the beach or at the park. I believe that the 7-speed bike is much more useable than the 21 speed.
The 21-speed bike is made for flat ground and steep hills. The 21-speed bike will allow you to conquer any hill you throw at your bike. It's got super low gear to take you up a real steep hill. You can also go really fast putting it in the highest gear. The 21-speed bike will be perfect for someone who has knee problems where they want real ease of pedal. You can put it in LOW gear and it won't even feel like your pedaling your bike but your bike is going. The 21-speed bike will be the "fastest/slowest" bike.