RUST. Very common that The small amount of rocks and sand have accumulated from rusty pipes, connections, and/or rusting water heater.
There is a clogging in the hot water heater water tank and/or its outlet line (left side ON the tank) by too much rust buildup in the water tank or outlet pipe (left side). This clogging of course can also lead into your pipes going to the faucets and shower.
Now...water heater, turn off the breaker (electric water heater) -or- turn off the gas supply line (gas water heater). Turn off water supply line on right side of water heater.
Let all water drain from bottom of tank by connecting water hose. If all water does not drain and seem trapped, then unscrew and remove the valve.
View elements that exited the tank (rust, corrosion, sand, small rocks). If much rust and other white elements have drained, then anti-rust magnesium anode rod has failed.
Close the bottom valve. Open the hot water valves in kitchen and bathroom(s). Refill the water within heater. When totally re-filled, turn on the breaker switch (electric water heater), -or- turn on gas supply line and light up the pilot and burner.
If brown water continues to coming thru pipes, then its time to replace the water heater.