An HRM will benefit you the most if you are training rigorously. In a nutshell, it can help you determine that you're riding hard enough on hard days, and easy enough on recovery days.

They're also useful for pacing yourself on long rides, i.e. that you're not overdoing or underdoing it. It's easy to go too hard early in the ride, and not conserve your strength/energy for later. By the same token, the HRM can help you determine that you are riding up to an effort level that you are capable of.