The muscles in your arms and legs are surrounded by fascia, thick tissues that seal them off into self-contained compartments. These fascia do not expand, but damaged muscles do expand -- they swell when they are damaged. If muscles swell too much, this will result in too much pressure in the muscle compartment, and can cut off blood flow, damage nerves, and lead to damage and necrosis of the affected muscles.
Most cases of acute compartment syndrome are caused by bone fractures, although it may also be caused by severe sprains or bruises, and may sometimes occur due to mechanical pressure (e.g., a cast that is too tight). It is most common in the forearm and lower leg, although you can also have cases that occur in hands and feet, thigh and buttocks, and upper arm. Acute compartment syndrome tends to be very painful and obvious; you are unlikely to voluntarily live with an acute case without seeking treatment.
On the other hand, chronic cases can be quiet mild, and may be evidenced only by moderate discomfort, e.g., numbness, a tingling sensation, a feeling of tightness, weakness, and/or pain, usually occurring immediately after exercise and fading with rest. Chronic compartment syndrome (usually referred to as CCS) does not usually indicate a fracture, only that you are regularly exercising in a way, or at an intensity, that your body is not prepared for. However, it can result in nerve damage if untreated, and may be treated incorrectly by non-professionals (e.g., a compression bandage would be counterproductive), so when in doubt, check with your doctor!
The primary symptoms of compartment syndrome are pain and loss of function (including range of movement, strength, and sensation), which is accompanied by localized swelling. Localized weakness (e.g., foot drop) is also a sign in CCS. In acute cases, pain is likely to be more severe than would be predicted by the underlying injury, and may not respond to painkillers.
Warning: do not Google compartment syndrome unless you have a high tolerance for gory images.