Brown stains on skin after working with Tollens' reagent
The stains are due to silver nitrate, the reactive portion of Tollens’ reagent. It is very prone to reduction to metallic silver.

If you got it on your hands (a clear signal you weren’t wearing gloves when you should have been) it will create small silver particles in your skin — this is why it won’t wash off. Since the particles are small, they don’t exhibit the classical metallic characteristics (looking silvery, reflecting etc).

Don’t worry, they will grow out within a week’s time or so, due to your skin renewing itself.
And wear gloves next time.