A sticking caliper is a brake that will not fully release, so it keeps dragging on the rotor. It is tempting to keep driving, but a stuck caliper causes real damage and safety risk. Here is why you should not ignore it.
What a sticking caliper does
When a caliper sticks - from a seized guide pin or a corroded piston - the pad stays pressed against the rotor even off the brake; see caliper slide pins. That constant drag makes that one wheel run much hotter than the others; see one brake running hot.
Why it is dangerous
The heat from a dragging caliper can boil the brake fluid at that corner, warp the rotor, and even smoke or catch fire in extreme cases; see warped rotor causes. The drag also pulls the car to one side under braking and kills fuel economy. It rapidly ruins the pad and rotor on that wheel.
Signs to watch for
A pull to one side, a hot wheel or burning smell after driving, reduced mpg, or a rotor that is blued from heat all point to a stuck caliper. You may also feel the car not coasting freely.
What to do
Stop driving on it and have the caliper freed or replaced; a rebuild or replacement is the fix - see caliper rebuild vs replace. Replace the damaged pads and rotor on that corner and fit fresh pads with new hardware.