Matthew 5:13 You are the salt of the earth: but if the salt have lost his savour, wherewith shall it be salted? it is thenceforth good for nothing, but to be cast out, and to be trodden under foot of men. 

Why does Yeshua use a word "the salt"?

In Israel there was "a covenant of salt" ("brit melah"):

Numb 18:19 All the heave offerings of the holy things, which the children of Israel offer unto the LORD, have I given thee, and thy sons and thy daughters with thee, by a statute for ever: it [is] a covenant of salt for ever before the LORD unto thee and to thy seed with thee.

2Chr. 13:5 Ought ye not to know that the LORD God of Israel gave the kingdom over Israel to David for ever, [even] to him and to his sons by a covenant of salt?

"A covenant of salt" is the law which was clearly formulated in Torah. (According to this covenant) it was necessary that salt would be in the Temple always. As the table (for food) of Jews is the altar, we use salt during the meal always too."
(Zeev Dashevsky Lectures Malachim (Russian translation) http://www.machanaim.org/tanach/_da_ml/ml_37.htm#v5)

Shaul said:

Col 4:6 Let your speech [be] alway with grace, seasoned with salt, that ye may know how ye ought to answer every man.

The salt has two characteristics:

- The purity;

- the flavouring

We believers in Messiah Yeshua need be both the pure ones and be by "the flavouring" for this world. 

Jam 1:27 ... to keep himself unspotted from the world.

In Mark we read:

Mark 9:49 For every one shall be salted with fire, and every sacrifice shall be salted with salt.

Mark 9:50 Salt [is] good: but if the salt have lost his saltness, wherewith will ye season it? Have salt in yourselves, and have peace one with another.

We believers in Messiah Yeshua MUST NOT LOSE our SALTINESS!