A jockstrap (or simply the jock, hence the slang term for athlete) is a kind of fabric underwear designed to hold a protective insert (usually plastic) to protect the crotch. The insert is often called a cup in the USA, or a box in Australia. SCA combat rules require a cup be worn at all times while fighting.
Cleanliness is very important when dealing with a jockstrap. "Jock itch" is an extremely uncomfortable fungal infection which can develop from an unsanitary jockstrap. Typically, it is best to wash the fabric jockstrap with a regular load of laundry, and separately hand-wash the plastic cup in hot, soapy water.
In the SCA the jockstrap-and-cup arrangement is euphemistically called the "most important piece of armour". Since it is worn in an intimate location, it is generally the one piece of armour not found in a collection of loaner gear.
A jockstrap is not quite the same as a codpiece.