In the NBA, a team has to hold cap space for their free agents until the player signs with a team or the team renounces the player's rights.
Cap holds are "placeholders" for players the team is expected to sign in the future. For example, a team is expected to sign its unsigned first round draft pick, so an amount is reserved for this signing in the form of a cap hold. A team $10 million below the cap with $4 million in cap holds therefore has $6 million in room. A team $5 million under the cap with $6 million in cap holds is not considered to be under the cap at all, and must use exceptions to sign players.
Once Bird rights are established, they don't go away unless the player is renounced or signs with another NBA team. This means teams retain Bird rights to many players who have long since retired, and could still use those Bird rights to re-sign such a player if that player attempts a comeback (but not for a sign-and-trade transaction
In the case of the Celtics, the last time they had cap space was in 1997 and so there wasn't a reason to go through the paperwork of renouncing a player. Now that they are under the cap, renouncing these cap holds will allow the Celtics to have even more room under the cap.