”You are”

In the Greek, Jesus is emphasizing the "you" part of this statement ("You, you are..."). He is making sure that we understand that it is solely the role of His followers, and no one else, to be the salt and the light of the world.

Salt — uses:

Preservation, purification (Ex. 30.35, Ez. 16.4)
herbicide or a destructive agent (Deut. 29.23, Judges 9.45, Psalm 107.33-34, Jer. 17.6, Zeph 2.9)
seasoning (Mark 9.49)

What function are we supposed to serve here?

We are to be the purifying agent of the earth and the preservers of the truth.
We cannot be the preservers of the earth, because the earth is corrupt and decaying.

“of the earth” – of (genitive of reference), meaning salt as far as the earth is concerned.

We are to be in the world, but not of the world.

“loses its flavor” –to be made foolish, to be defiled.

This expression suggests an Aramaic background.
What happens as a result of this?
If we lose our saltiness - or purity - how will we be purified?
When we lose our purity, we become counter-productive, and we become an agent of destruction rather than healing and purifying.

“thrown out and trampled underfoot” (katapateo) – walked around on, trampled with scorn and shame

When salt became impure or mixed with sand, it was good for nothing but to be thrown out. It could not even be thrown in the dung heap because it would destroy what little value that the dung had as fertilizer, because it would kill the grass.
Therefore, it must be thrown on the heavily beaten path, where nothing grows anyway. There, the “salt” becomes an object of scorn, because all it will do is destroy.

Light — Isaiah 9.1-2, Matthew 4.15-16

giving hope, and joy to those who are in darkness and gloom.

The City on a Hill: The glow of a city upon a hill in the night skyline.

A Lamp: in complete darkness (minus electricity) the slightest light is sufficient for all who are in the house.

“Let your light so shine”—before men, in the presence of, in front of men.

To glorify God our Father, not ourselves. This idea counters the exaggeration (by many) of chapter 6, saying that all good works should be hidden.
This is not righteousness for the sake of being righteous, nor is it righteousness in order to be seen by men. It happens that we are seen while obeying our Master and Lord while we are in this world.

Ultimately, Jesus is calling us to remain pure and unmixed with the world so we do not lose our purifying and preserving function on the earth through the clear and faithful proclamation of the true gospel. He is calling us to also proclaim the gospel with hope, love, and grace, so that the world would see what we do and how we treat them, and give glory to God our Father.