Albert Barnes Commentary Matthew 5:13

"Ye are the salt of the earth: but if the salt have lost its savor, wherewith shall it be salted? it is thenceforth good for nothing, but to be cast out and trodden under foot of men." — Matthew 5:13 (ASV)

Ye are the salt of the earth. Salt makes food pleasant and palatable, and preserves it from decay. So Christians, by their lives and teachings, are to keep the world from complete moral corruption. By bringing down God's blessing through their prayers, and by their influence and example, they save the world from universal vice and crime.

Salt have lost his savour. That is, if it has become insipid, tasteless, or has lost its preserving properties. The salt used in this country is a chemical compound—muriate of soda—and if the saltiness were lost, or it were to lose its savor, nothing would remain. It enters into the very nature of the substance. In eastern countries, however, the salt used was impure, mixed with vegetable and earthy substances, so that it might lose all its saltiness, and a considerable quantity of earthy matter would remain. This was good for nothing, except that it was used, as it is said, to put in paths or walks, as we use gravel. This kind of salt is still common in that country. It is found in the earth in veins or layers, and when exposed to the sun and rain, it loses its saltiness entirely.

Maundrell says:

"I broke a piece of it, of which that part that was exposed
to the rain, sun, and air, though it had the sparks and
particles of salt, yet it had perfectly lost its savor.
The inner part, which was connected to the rock, retained
its savor, as I found by proof."

Compare Mark 9:50 concerning salt of the earth.