Salt is a universally understood symbol. Salt is used from time immemorial for purification, preservation and to make food palatable. Salt can preserve anything from humble lime to the mummies of great Pharaohs. Egyptians stuffed the bellies of the dead bodies with salt to remove the water and other liquids from the body. Then they applied salt along with other chemicals to preserve the corpses for millennia. Cooks all over the world add salt to food to make it palatable. 'Salt to taste' is that line which is so common in all recipes.
Jesus was defining the presence that his disciples should make in the world. They will be those who purify the world that they live, they will make life more palatable, and preserve what is valuable and noble than pull it down.
'Salt' also meant something more. In the Jewish thinking, to be precise in the writings of the Rabbis, salt is a symbol of wisdom. That is why Paul, one of the greatest Rabbis exhorted the Colossian church, 'Let your speech always be gracious, seasoned with salt, so that you may know how you ought to answer each person' (Col 4:6). The followers of Christ has to be full of wisdom so that their words are gracious and filled with wisdom.The idea of wisdom is explicit in the contrast that Jesus makes. The salt can lose its saltiness and become 'tasteless.' In Greek, the word used for 'tasteless' is same as 'foolish.' The disciples have two options. First, be salt or be wise. Second, be tasteless or be foolish!
Jesus reminds us of the great task that is ahead of us who live in this tasteless world. Life is miserable for many. Poverty, deprivation, injustice, lack of inner peace, conflicts within and without make our world unpleasant. The presence of the followers of Christ in this world that has lost it taste makes it more palatable.
The world is losing the values that preserve the human race. Values like respect for life, the dignity of the human being are being eroded among many other. Great social institutions like marriage and family that have preserved our race so far are under attack. The world is losing its salt. The disciples have to enter the world and salt it again with their presence. The Church thus has the great responsibility to make the world more palatable, or liveable. The world needs wisdom to live. That wisdom is entrusted in the Church of Jesus Christ.
However, the followers of Jesus can also lose their saltiness. Salt if not used could also react with other active chemicals and become something else even harmful chemicals. Just as salt that has lost its saltiness is thrown away and is trampled upon, the disciples who lose their saltiness will become laughing stocks before the world. That would be terrible.