Diagnosis
That means the charger base thinks a toothbrush is still attached. It's typically caused by a fault inside the base's sensing circuit.
How to Fix It
Unplug the charger from the wall outlet. Wait about 30 seconds, then plug it back in. Often, this quick reset will clear the glitch. If the light goes off when you plug it back in (without a handle on it), you're good. If the solid red light comes right back on with no handle, the base is likely defective.
If That Didn't Work
Before you condemn the base, check the charging contacts on the base itself. If there's a lot of built-up gunk, it might be conducting just enough to trick the base. Give those contacts a thorough clean with alcohol and a cotton swab, let it dry, and try again.
Heads Up
A charger base with a stuck-on light isn't dangerous, but it is wasting a tiny bit of electricity. It's best to unplug it when not in use if it's malfunctioning.