Brakes won't release after being applied?
Brake calipers have return springs to move open the caliper arms after closing force supplied by the force on the brake cable from the levers is removed.

If the calipers are not opening there are several things that can cause this:


Return springs are too weak
Caliper pivots stiff or jammed
Brake cable friction is preventing it from retracting through the housing, either due to contamination or poor routing.


Many linear pull or V-brake calipers have return spring adjustment screws near the pivot. You could try increasing the return force and see if that sufficiently opens the calipers.

Disconnect the cable from the calipers. With the cable removed do the calipers move freely? If you close the caliper arms by hand is there a reasonable return spring force opening them?

If the calipers look OK, try cleaning and lubricating the cables as in mattnz's answer.