The phrase "covenant of salt" (Numbers 18:19, 2Chronicles 13:5) or variation thereof (Leviticus 2:13) occurs only three times in the Bible. A covenant is an agreement between two or more parties. An agreement that involves salt symbolizes one that is meant to be perpetual, not corruptible and indissoluble.
The most well known reference to a covenant of salt is in relationship to God's promise to King David to make him a perpetual throne (2Samuel 7:11 - 16). The phrase itself was used at the start of King Abijah's taunts hurled at Israel's King Jeroboam for his hubris in planning war against the Kingdom of Judah.
Don't you know that the Lord God of Israel gave the kingship over Israel to David and his descendants forever by a covenant of salt? (2Chronicles 13:5, HCSB).
Why sodium?
Sodium has certain properties and beliefs surrounding its use that easily lends itself to certain symbolism in the Bible.
From the time of Adam, the most common way the average person could preserve the edibility of food, especially meat, was through salt. Its ability to maintain the integrity of food and retard spoilage was well known. This is likely the reason why God, in underscoring his enduring promise to always take care of or preserve the priestly tribe of Levi, labeled it a "permanent covenant of salt" (Numbers 18:19).
In the Near East, this expensive commodity was considered indestructible in fire. Under ancient Israel's sacrificial system, it was a critical element in offerings made to the Lord. Its inclusion was mandatory for all offerings (Leviticus 2:13, Ezekiel 43:24), no doubt symbolizing the eternal and indestructible covenant God made with his people.
This mineral also impedes the action of yeast (leaven) on food. In Scripture, leaven many times symbolizes sin and a rebellious attitude, as well as the ability to negatively influence others (1Corinthians 5, Galatians 5:9). The inclusion of the mineral, therefore, can represent the preservation and maintenance of purity in a world that can cause corruption.
In conclusion, the meaning of a salt covenant is an agreement that is meant to endure regardless of the circumstances. It was an ancient symbol of unbreakable friendships and alliances that were to be preserved. Such agreements are solid, unbreakable and everlasting.