As with verse 12, the beginning of this verse differs from Matthew 5:13.
Matthew: “Ye are the salt of the earth.”
3 Nephi: “Verily, verily, I say unto you, I give unto you to be the salt of the earth.”
The addition in 3 Nephi appears to be related to a difference in the audience. The address is slightly different, but the essential meaning is unchanged.
Why are the people who are listening to Jesus, in either hemisphere, the “salt of the earth”? The ancient world valued salt much more highly than do modern societies, for we have discovered ways to produce it in such quantities than none who desire it would lack it. For ancient Rome, it was valuable enough that wages were declared in units that would be required to purchase salt.
So, the people are being told that they are valuable, but that isn’t all. If we season with salt, we do not use much. Thus, the people are valuable, even if they are few, even if they are not the majority in the populations around them.
As for losing flavor, if there are impurities in the salt, then it loses its ability to be salty. Thus, Jesus is admonishing this small group of believers to remain pure and faithful so that their value to the world might be fulfilled.