What are these cloth covered wires?
In answer to your question the wires you are looking at are part of a cabling system known a BX. It is a lot like AC or MC only it doesn't have a grounding conductor and the conductor insulation is a type RH or RHW which is a rubber insulation wrapped in cloth. The other cloth is just fill.

This type of wiring was used in the late 1940's, 1950's and early 1960's until a more modern plastic insulation type offered better protection. Bx was known to be the cause of some fires during its use and was outlawed in many municipalities. One because as you can see there was no anti-short bushing (sometimes referred to as red devils and other names), which cut the insulation and started a high resistance short. Also when exposed to harsh (outdoor) environments or high heat at a junction it would dry out and crack exposing the bare conductor. Also as I have mentioned before there was no acceptable ground connection. 

I wouldn't go so far as to say this type of system is alright, but the key is the insulation if it is still malleable and covers the conductor well it should be OK. If it shows any sign of drying out and cracking it should be replaced, and if you are reconnecting it back up use the anti-short bushings to protect the wire. 

Stay safe.