Suspension Systems
Suspension allows the fork and/or the rear triangle to compress when a rider goes over a bump. This helps the wheels maintain traction in rough terrain and improves rider comfort. Suspension seatposts and stems are also available for rider comfort, but they don't assist with traction.
On road and most gravel bikes, the tires deliver sufficient suspension for the terrain these bikes traverse. In contrast, mountain bikes are designed to excel on rougher terrain. Almost all MTBs have at least front suspension, aside from those who elect to run rigid MTBs. The image below shows a sample of suspension forks.
Front suspension
Typically, in Cross Country (XC), All Mountain (AM), Enduro or Aggressive Hard Tail frames (ie, those that have no rear suspension), front fork travel can range from 100mm to 160mm travel dependent on the frame geometry.
Modern forks offer a lockout (also available as a remote lever lockout, mounted to the handlebar) which allows the rider to quickly disable the fork travel. This is useful when riding on road to provide a rigid platform so as not to unduly waste rider effort.
Rear Shock
(source: bouncecycles.co.uk)
Typical rear shock travel for mountain bikes ranges from 100mm to 200mm depending on the frame discipline with Down Hill (DH) bikes offering the most travel (+/- 200mm front and rear).
Previously, some bikes had a soft-tail suspension, with a shock unit placed where the seat stays attached to the seat tube. These typically had smaller travel.
Similarly to front suspension, some rear shocks offer a travel lock out which limits the rear shock travel, useful for riding on tarmac or more predictable surfaces.
Some key concepts Suspension systems can be sprung by:
Coil-sprung shocks use a large metal spring – normally steel – positioned outside the telescopic tubes that make up the shock body.
Air-sprung shocks meanwhile feature a compressed air spring inside the body of the shock.
Elastomer-based systems rely on rubber or another elastic material to compress. These typically offer less travel than coil shocks, but are lighter.
Some key terms are:
Travel: the maximum distance which the suspension can travel. Very roughly speaking, more enables you to handle rougher terrain.
Bottom out and top out: When you hit a bump, if the suspension system reaches the limit of its travel, it has bottomed out. If you have too many harsh bottom outs, you need more suspension and you also risk damaging the suspension. Conversely, a suspension system will rebound after taking a hit, and top outs occur when it hits its travel limit on the rebound. Suspensions may have rubber bumpers inside the suspension chambers to prevent damage if it bottoms out.
Sag: When you sit on the bike, your weight compresses the suspension. This is called sag. Suspension systems can be tuned for riders of different weights. Notably, suspension manufacturers may recommend that you set the damping such that the sag is a certain percent of the total travel.
Compression damping and rebound damping: You can adjust suspension, e.g. by adding air pressure, to adjust its feel while compressing. More compression damping means more resistance as the fork compresses, which feels firmer. You can similar adjust the amount of rebound damping.
Maintenance
Suspension systems require periodic maintenance. Riders should wipe their fork stanchions, or the metal legs, after each ride, and inspect for scratches. Periodic higher-level maintenance may involve replacing the fork seals, which keep dirt out of the suspension chamber, lubrication, possibly rebuilding springs and replacing bushings.
Newer cyclists riding only on paved paths should consider foregoing a suspension system. The prime reason is that suspension is not necessary for this use case, and furthermore a suspension fork requires maintenance and will eventually seize without maintenance - at which point it is dead weight that you paid extra for.