A cap is synonymous with a call option, ensuring its buyer protection against a rise in the underlying (in this case, the chosen reference rate) above the strike.
A cap actually consists of a series of options, also known as caplets. Each caplet successively ensures the buyer protection for a single payment period. That is, if on the caplet's fixing (or caplet) date the reference rate is above the strike, on the payment date at the end of the payment period the cap seller pays the buyer a payoff as follows:
(reference rate - strike) * notional * relevant daycount fraction
Usually the reference rate is set in-advance, i.e., it is set at the start of each payment period and paid at the end of that payment period. However, it can can also be set in-arrears.
In return for this protection, the buyer of the cap pays a premium to the seller. Expressed as a percentage of the notional, the premium is usually paid upfront. However, it can also be paid in instalments over the life of the cap.
Why is being able to pay the premium in instalments a useful feature? Corporates typically like to pay the premium for a cap/floor in installments. This means that instead of paying for all of the options upfront (remember that the cap/floor is basically a series of European options), they can spread the cost over many periods and arrange it so they pay for the specific option when it is actually used, i.e., on each caplet/floorlet payment date. Paying the premium by installments is simply a loan the cap/floor seller is making to the cap/floor buyer. In some cases, the seller will not have credit lines with the buyer; if this is the case, the seller cannot allow the buyer to pay by installments. Customers who are not cash sensitive will typically pay upfront for the option.
Example of a cap:
You buy a cap based on 3-month LIBOR with a strike of 4%, on a notional of $1,000,000. On each caplet date, you will receive money if the 3-month LIBOR is over 4%. If on a caplet date the 3-month LIBOR is 5%, you will receive the following:
(5% - 4%) * $1mio * (3months/1year) = 1% * 1/4 * $1mio = $2,500
Advantages of a cap
Because it acts as an upward hedge, buying a cap lets you hedge yourself against a rise in the reference rate for a specified period, while giving you the flexibility to benefit from any reduction in the same reference rate.