Bicycle forks come in two main variants; Suspension & Rigid. Suspension forks typically fit on a mountain bike or hybrid bike, while a rigid (solid) fork would usually fit a town-style bike, which is expected not to have to deal with too many bumps on rough terrain. Suspension helps with soaking up the pressure of bumps and hits, whereas a rigid fork will have reduced weight.
Air or coil sprung offer different feelings when compressing and rebounding. An air fork is considered to be better and is typically more expensive than coil. A coil sprung fork can be non-adjustable, or have features like lock-out and rebound control. Air forks will likely have lock-out and rebound control as a minimum. This allows you to switch between rigid and functional suspension (lock-out) and also to allow control of the spring-back speed (rebound.)
