The spidery patterns in turquoise are remnants of the host rock in which the mineral formed. Correctly known as matrix, they can be black or brown and can help identify the stone as being turquoise.
Turquoise is relatively soft and fragile so must be well looked after. It should not be allowed to get wet. Pollutants in the atmosphere including perfumes and hairspray can leave a residue which could be difficult to remove.
Wiping a stone before and after it's worn and keeping it covered whilst stored away can help prevent unwanted marks and scratches.