To constrict is to squeeze uncomfortably. If your new turtleneck sweater constricts your neck, the sweater is probably too small.
When things constrict, they become narrow or make something else become narrow. A boa constrictor kills its prey when it constricts the animal's body until it can no longer breathe, and a necktie that's tied too tightly constricts your neck. In medicine, certain conditions or medications can constrict openings such as airways or blood vessels, sometimes dangerously. The Latin root is constringere, "to bind together or tie tightly."