to make fast by tying: to bind, fasten, harness, or hold a person or thing in restraint
The picture under every use of this word is the same: something is held fast by a cord, a chain, or a tie. From that one image the word reaches in three directions. Most plainly it ties one thing to another, harnessing an animal to a chariot or fastening an offering to the altar.
From tying a thing it moves to holding a person, binding a captive or shutting a prisoner away in chains. The same act that secures a load is the act that takes away a person's freedom, so the word does double duty for harnessing and for jailing without changing its core.
It then turns inward. A person can tie themselves down with a promise, taking on a binding obligation by their own word. Here no rope is involved, yet the logic is identical: the vow holds the person as surely as a cord holds an animal, and the word for the cord is the word for the commitment. The three senses are one act of binding seen against a thing, against a captive, and against one's own will.