to be firm, steady, and reliable, so that a person or thing can be counted on
This is the root idea behind the whole word: something that holds firm and does not give way, so you can lean your weight on it. The same picture covers a person who proves dependable, an office or promise that stands, and a structure fixed solidly in place.
When it describes people it means faithful or trustworthy: a servant, a priest, a witness, or a friend who can be relied on. When it describes God's promises, his covenant love, or a royal house, it means lasting and secure, fixed so firmly that time cannot shake it. When it describes words or testimony it means confirmed and proven true.
These shades are one idea seen from different angles. A faithful person, an enduring promise, and a verified report all share the same quality of being solid and dependable rather than shifting or failing.