Cucumber tests share the benefit of traditional specification documents in that they can be written and read by business stakeholders, but they have a distinct advantage in that you can give them to a computer at any time to tell you how accurate they are. In practice, this means that your documentation, rather than being something that's written once and then gradually goes out of date, becomes a living document that reflects the true state of the project.
Source of Truth
For many teams, they become the definitive source of truth as to what the system does. Having a single place to go for this information saves a lot of time that is often wasted trying to keep requirements documents, tests, and code all in sync. It also helps to build trust within the team, because different parts of the team no longer have their own personal versions of the truth.