To tighten something is to draw it snug or squeeze it. Your cousin's crazy driving may cause you to tighten your seatbelt and close your eyes.
You can tighten things literally, the way you tighten the lid of a jar or tighten your hold on your best friend's hand as you enter a haunted house together. There's also a figurative way to tighten, like when a library tightens its rules about talking or a restrictive government tightens control over what newspapers are allowed to print. Before tighten appeared in the 18th century, the verb was tight.