This idea alludes back to the prophecies in Daniel 2 and 7, where God establishes a kingdom that will never be destroyed. This is in contrast to the other kingdoms that had been on the earth, that existed for a time and were ruled by greater and lesser kings, but were all eventually destroyed.
In Daniel 2, king Nebuchadnezzar has a dream during the night, but when he awakes he is unable to remember what it was about. No one is able to tell him what his dream was except Daniel, who describes the dream and then gives the interpretation of it:
36 “This is the dream. Now we will tell the interpretation of it before the king. 37 You, O king, are a king of kings. For the God of heaven has given you a kingdom, power, strength, and glory; 38 and wherever the children of men dwell, or the beasts of the field and the birds of the heaven, He has given them into your hand, and has made you ruler over them all—you are this head of gold. 39 But after you shall arise another kingdom inferior to yours; then another, a third kingdom of bronze, which shall rule over all the earth. 40 And the fourth kingdom shall be as strong as iron, inasmuch as iron breaks in pieces and shatters everything; and like iron that crushes, that kingdom will break in pieces and crush all the others. 41 Whereas you saw the feet and toes, partly of potter’s clay and partly of iron, the kingdom shall be divided; yet the strength of the iron shall be in it, just as you saw the iron mixed with ceramic clay. 42 And as the toes of the feet were partly of iron and partly of clay, so the kingdom shall be partly strong and partly fragile. 43 As you saw iron mixed with ceramic clay, they will mingle with the seed of men; but they will not adhere to one another, just as iron does not mix with clay. 44 And in the days of these kings the God of heaven will set up a kingdom which shall never be destroyed; and the kingdom shall not be left to other people; it shall break in pieces and consume all these kingdoms, and it shall stand forever. -Daniel 2:36-44 (NKJV)
The final kingdom that God establishes on the earth breaks and consumes all others. The destruction of the other kingdoms is so great, that it is compared to their remains becoming like chaff and being carried away by the wind:
Then the iron, the clay, the bronze, the silver, and the gold were crushed together, and became like chaff from the summer threshing floors; the wind carried them away so that no trace of them was found.... -Daniel 2:35 (NKJV)
In Daniel 7, the final kingdom is again contrasted with the others as being the one that will never be destroyed, with the "Son of Man" being the one to rule the kingdom:
13 “I was watching in the night visions,
And behold, One like the Son of Man,
Coming with the clouds of heaven!
He came to the Ancient of Days,
And they brought Him near before Him.
14 Then to Him was given dominion and glory and a kingdom,
That all peoples, nations, and languages should serve Him.
His dominion is an everlasting dominion,
Which shall not pass away,
And His kingdom the one
Which shall not be destroyed. -Daniel 7:13-14 (NKJV)
As Steve Taylor said in his answer, Jesus is the King of Kings and Lord of Lords because, since He is so much greater than any previous king and lord ever was, the title of just "King" and "Lord" is not fitting.