Investors and companies utilizing accrual swaps assume the risk that the reference rate will stay in a certain range. The broader the lower and upper cap, the greater the risk that the reference rate will fall within this range, which is typically what is desired since interest will not be accrued.
For example, a company with a floating-rate obligation denominated in euros wants to hedge its exposure by paying a fixed rate which is below the market rate. The floating rate is conditional on how many days EURIBOR is within an agreed upon range during a set period. The goal of the company is to obtain a lower fixed rate by assuming the risk that the EURIBOR rate will fall outside of the agreed upon range.