When hiring, just from an employee's history I am probably 3 degrees or less away from being able to contact every one of their old bosses. Given this I can get a very clear picture of what an employee really did, as opposed to what they claim they did on their resume.
The second reason to use them is as a filter. Can't provide any references, that's a big huge giant red flag. If you can't find one person to vouch for you that's not a positive signal.
For other industries like lawyers, doctors, and engineers, as you become more senior, your value switches from being 100% dependent on your work ability to the value of your professional network.
ie an experienced doctor/engineer/lawyer brings with them a network of clients, and other professional contacts that may be worth 10x what they can do in their given profession.
As a non practicing engineer, that was one of the biggest eye openers to me. The fact that your professional network can have more value than your professional abilities.
Think of the example of say Mark Zuckerberg, imagine you were going to hire him.
What's more valuable, his ability to get pretty much any person to help move your company forward or his ability to code?
I'd say its the former, and its the former by a long shot.
Where reference checks are pretty useless is when hiring a new grad or someone who is switching fields. In those cases you aren't likely to get any positive benefit from reference checking.