Two hardware vulnerabilities have been recently revealed, and they affect the CPUs (brains) of most modern computers and electronic devices. The only permanent fix is replacing the affected hardware but there isn’t anything available just yet. It’s going to take some serious work by hardware vendors to come up with a solution. That being said, software patches are being made available, so go ahead and perform any updates that become available for your computer, phone, tablet, and all other electronic devices as soon as possible.
Since this affects pretty much all computers, your website may also be rebooted during the patching process. Contact your web host with any questions.
Full details, in human-readable form (!) are on the Defiant blog: The Impact of Meltdown and Spectre Vulnerabilities