What's the next step in Disk Utility?

I have a desktop using OSX... something. I'm sorry. I haven't paid attention to that in a long time and I'm not confident that I know the answer. That said, I usually update when my computer asks me to. So if I'm not fully updated, I think I'm close.

I was listening to music and my computer started skipping (like a cd would). Then it turned off by itself. Less than a minute later it started turning off and on by itself several times and then the screen turned blue.

I shut it down with the power button and powered it back up with the command and R button pressed and got to Disk Utility. I then hit Verify Disk and it said the Mac HD is okay. Then I hit verify permissions and repair disk permissions.

Now it says, Permissions Repair Complete.

I did all of this from web tutorials and have no idea what I'm doing. I actually don't even know if I'm posting this to the right group 😕

The tutorials were kind enough to get me this far but now what? Do I just shut down/restart? Some tutorial said something about opening in safe mode but I couldn't tell if it applied in this situation.

I would really appreciate some guidance here. I'm under a deadline and was _just about_ to start working when this happened!

Please help!