Just sent in via press release from the Kings:

 The Sacramento Kings today renounced the rights to Samuel Dalembert (center), Pooh Jeter (guard), Marquis Daniels (forward/guard) and Darnell Jackson (forward), according to Kings’ President of Basketball Operations Geoff Petrie.

So what does this mean?  NBA Salary Cap Expert Larry Coon has the answer:

By renouncing a player, a team gives up its right to use the Larry Bird, Early Bird, or Non-Bird exceptions (see question number 19) to re-sign that player. A renounced player no longer counts toward team salary, so teams use renouncement to gain additional cap room. After renouncing a player, the team is still permitted to re-sign that player, but must either have enough cap room to fit the salary, or sign the player using the Minimum Salary exception. The exception to this is an Early Bird free agent who is coming off the second season of his rookie scale contract. Such players, when renounced, are treated as Non-Bird free agents.

Further explanation from Cowbell Kingdom’s James Ham:  Samuel Dalembert had a free agent cap hold figure of $19,045,250.  The combination of Darnell Jackson, Pooh Jeter and Marquis Daniels had an additional cap hold of approximately $4.8 million, taking the Kings’ cap figure from roughly $32 million, to close to $56 million.  By renouncing the rights to Dalembert, Jackson, Jeter and Daniels, the Kings freed up their cap holds, enabling the team to sign the contracts of Marcus Thornton (estimated 5-yr/$40 million) and Chuck Hayes (estimated 4-yr/$21.3 million).

What does this mean?  The Kings no longer have Larry Bird rights to any of the four waived players.  All four could be retained as unrestricted free agents, but the maximum length of any deal signed would be four years, instead of five.  The Kings also relinquished the right to use any of these players in sign and trade transactions.