In my own understanding Davidic Covenant is the promise which was made long time ago to Juda the great grandfather of David and it was stated as follows: The scepter shall not depart from Judah, nor a lawgiver from between his feet, until Shiloh come; and unto him shall the gathering of the people be, Genesis 49:10 and David inherited that promise because it was pointing to Christ.Again the promise was also passed to Solomon since it was an everlasting covenant. It was fulfilled in Jesus Christ when the angel announces the birth of Christ to Mary and we read from Luke 1:31-33 "And, behold, thou shalt conceive in thy womb, and bring forth a son, and shalt call his name JESUS. He shall be great, and shall be called the Son of the Highest: and the Lord God shall give unto him the throne of his father David: And he shall reign over the house of Jacob for ever; and of his kingdom there shall be no end."
When Christ comes back for the second time,the kingdom will be forever and we read that in Revelation 5:5,"Then one of the elders said to me, 'Do not weep. See, the Lion of the tribe of Judah, the Root of David, has conquered, so that he can open the scroll and its seven seals.