I can see three main benefits.
Reduce the amount of passwords users have to remember. Users are encouraged to use vastly different passwords for different sites. Managing that many different passwords can be problematic. Obviously this isn't an issue if the user uses a password manager tool but let's be realistic, how many users can you expect to do that? A SSO solution can greatly reduce the number of passwords a user has to remember, which might encourage the user to choose a much stronger password.
Provides convenience to the users. A SSO solution literally means the user has to sign on just one single time to access multiple services. This is a huge timesaver especially if a company provides multiple services. A good example of this would be Google. While this might not strictly be accurate, I have a feeling that by reducing the number of times a user has to enter his credentials, the risk of an attacker intercepting the credentials through something like a keylogger will be reduced.
Reduce the headache of assisting users with password recovery. Imagine a company running ten different services. A SSO solution can greatly reduce the amount of helpdesk manpower needed as users only need to recover a single account. Whilst not a security concern, this is a very tangible benefit to companies.
Of course, a SSO solution concentrates a lot of power on the authentication solution. One should probably spend a lot more time and effort securing that single point of failure.