What are these cloth covered wires?

That is Armored Cable, or commonly called BX which is a brand. Its from before the widespread use of modern polyethylene and synthetic plastics for insulation on wires. The copper wires in the BX cable are coated in rubber and wrapped in cloth. The issue over time is the rubber becomes dried out, brittle and crumbly. Once its moved around or bent then it can easily break open. Its fine as installed but you should be careful as you work with it. Its easy to crack and then short if anything comes in contact with the copper wire. When bending the wires into a new box you may notice a crack and should wrap that in electrical tape. Your picture is a 3 conductor cable, probably used on a fixture that had a 3-way switch. Black hot, White Neutral, Red is traveler.

The metal sheathing of BX cable is the grounding conductor, and this type of cable should be clamped to a metal box. Then your fixture grounding is connect to that metal box or the housing is metal and screwed to the box. It looks like in your picture this isn't a box installed anymore, and there is a Romex cable in the mix. If you intent to keep the BX cable, you'll need to connect the grounds together somehow, such as install a metal box, clamp the metal sheathing into the box, and connect the bare copper ground from the Romex and copper ground wire from your fixture to a pigtail anchored to the metal box.

It's an earlier type of armored cable referred to in the day as BX -- common in the early-mid 1900s. We have a ton of that stuff in my house. The wires are insulated with rubber and cloth (they started using modern PVC insulation in the 1950s). Code dictates that metal boxes and any exposed metal parts in the wiring system be grounded. The outer metal sheath was kept at ground potential by using metal boxes throughout the system, starting at the panel, hence grounded outlets can be installed on existing circuits using this type of cable (as opposed to knob-and-tube or old Romex without a ground conductor) as long as the ground continuity through the armor back to the panel checks out okay (can be verified by using an outlet tester). So, based on the picture, I can say confidently that your house was wired prior to the 1960s. I would try bending the wires and see if the insulation cracks. If you're concerned and want 100% peace of mind, install AFCI/GFCI breakers (assuming you have a modern circuit breaker panel).