A 360 command can be sent by either Tower or a radar frequency. It’s generally used to create more spacing, descend an aircraft down further at their present position, etc.
The pilot will either need to make “left 360”, which means they turn left 360 degrees in a circle, or “right 360”, which means they will turn right 360 degrees in a circle.
After the 360 they’d continue on their previously assigned heading, but the radar controller should send a heading instruction to avoid confusion.
For Tower, all they’d need to do is wait for the aircraft to finish their 360, the pilot should continue inbound afterwards but if they do not a “continue inbound” wouldn’t hurt.