The Covenant of Grace

The Covenant of Grace is that arrangement whereby God planned to save elect man from the just consequences of his sin; namely, immorality, misery, death, and damnation.
While that is a very concise rendering of the definition of the COG, it would be wise to unpack this sentence somewhat:
The word "covenant" means a disposition or an arrangement. This arrangement was made by God alone. This covenant was made in eternity. Man had no part in its making.
The word "grace" essentially means undeserved favor. The grace of God is divine favor manifested to sinners who deserve just the opposite: his disfavor and wrath.
So, the Covenant of Grace is that arrangement whereby God planned to save elect man from the just consequences of his sin; namely, immorality, misery, death, and damnation.
The main condition for covenant of Grace is Faith.