If only out of the hot water faucet, then unless you have had an good earthquake lately or water outage that shook pipe buildup loose, something is definitely going on. Check all hot water faucets - if brown at one then you have a pipe corrosion problem at that faucet or pipe only. If brown at cold and hot both, then corroded pipe issue, or incoming water is dirty. If only at hot but all hot faucets, see below.
Hard to diagnose, but I would guess you have not been draining off 5-10 gallons of water from the drain valve every year or less. While it is possible a slab of rust and scale buildup broke loose from the wall of the tank and fell, dirtying the water, probably what has happened is enough lime and rusty scale buildup has accumulated in the bottom of the tank that it acts as an insulator between the firebox and the water, so you have got boiling going on there (assuming a gas heater, here), stirring up the bottom "mud". Another possibility is a corrosion protection anode corroded away and dropped into the bottom of the tank, stirring up the mud. The first would be an on-going issue, the second one-time but of course you would then have only have half as much corrosion protection, or zero, depending on whether you have 1 or 2 anodes.
You could try flushing out the tank with the drain valve and a hose, but with a 20 year old tank you are really pushing your luck - it is quite possible that will expose seriously rusted spots that will then start of leak in a quite short time - commonly within weeks. Normal tank like is 10-15 years - few make 20.You could flush it and hope for the best - if in a crawl space or basement where a leak would do no harm, then maybe let it go after draining out the gunk. If a flood would hurt flooring or finished walls, then probably better not to chance it.
I would bite the bullet if you can and just replace it, because you could spent several hundred $ trying to track the issue and be nowhere further. Look in Browse All Questions - one of the first ones, has about 49 answers, deals with cost.