Covenant -> Ark Of The Covenant -> The Covenant is an ark.
The covenant is the Ten Commandments. It is the set of rules the Israelites accepted upon themselves when accepting God. It was the deal the two parties struck - God would help and provide for the Israelites, if they follow the ten rules he had written down for them. The ark in "Ark of the Covenant" is just the golden chest in which the Ten Commandments are stored. The chest in itself is worthless (other than, perhaps, its value in gold) - what's important is what's inside.
Which is exactly why the symbolism in Alien:Covenant is so shallow: The Covenant was the holiest artifact in the Israelites' possession, while the film features several instances in which the crew of the ship is shown to not give a flying f**k about the ship's cargo. The symbolism doesn't work beyond 'Here's a biblical term I recognize!'