It could be a couple of things, but they aren't good.
The least serious is a cable is getting hit by fan blades, and that wouldn't happen within the PSU. You can find it fairly easily if this is the case.
It could also be a fan bearing going out. If this is the problem, you can identify the one that's about to go by feeling around the fans. If any are vibrating particularly strongly, you can tap on it to see if the buzzing stops. If it does, it probably has some variation of a sleeve bearing, and it's on it's last leg. Order a replacement. If it doesn't stop, you just need to wait until the noise does stop, and feel around again. The problem fan would be shaking noticeably less when the noise isn't present.
If it's coming from within the PSU, replace the PSU. It's about to go. You might have a week, two months, or a few hours of life left in it.
If it's a hard drive, back it up ASAP. Same deal as with the PSU.