What is "the stone that the builders rejected"?

What do the words, “Whosoever shall fall on this stone shall be broken” (Matthew 21:44) imply?

Psalms 118:22  The stone that the builders rejected has become the cornerstone.
Matthew 21:42-44  Jesus said to them, "Have you never read in the Scriptures: "'The stone that the builders rejected has become the cornerstone; this was the Lord's doing, and it is marvelous in our eyes'?  (43)  Therefore I tell you, the kingdom of God will be taken away from you and given to a people producing its fruits.  (44)  And the one who falls on this stone will be broken to pieces; and when it falls on anyone, it will crush him."

The meaning seems to be clearly given in such passages as Isaiah 8:14-15; 1 Peter 2:7-8; and Romans 9:32-33. Those who reject the Gospel (especially Israel), instead of building on the “Living Stone” of 1 Peter 2:4, stumble and fall over the “Stone of Stumbling” of v. 8.
The whole picture in Psalm 118 and Matthew 21 is very interesting. The Stone was meant for the foundation, but the builders did not place it there and afterwards could find no place to fit it. So they “rejected” it and cast it aside. Then as they moved about at their work, it lay in their way, and they stumbled over it and fell. Lastly, God Himself takes up the Stone and places it in the most conspicuous place of all, as “Headstone of the corner,” and the rejected One becomes the Judge and Punisher of those who rejected Him.