A somewhat long-winded explanation:
Last summer, when the Celtics traded away Garnett, Pierce, and Allen, they sent out significantly more salary than they took back. Specifically, as part of the deal they sent Paul Pierce (~$15 million) for Keith Bogans (signed and traded for $5 million). This resulted in the creation of a Traded Player Exception ($10 million).
The Celtics have one calendar year from the date of the finalization of that trade to use this Traded Player Exception, plus a grace period of a few days.
The Traded Player Exception allows the Celtics to take on salary in a trade without sending equivalent salary back, even though they don’t have room under the cap to do so. However, the Traded Player Exception can only be used to absorb the salary of one player, not multiple players, and it can’t be broken up into smaller chunks in separate deals. The Celtics can use it once, and only once, on one player.
An example of a deal the Celtics could pull off would be to absorb Jeremy Lin’s salary from Houston without sending anything in return. For the service of taking on Lin, the Celtics can get the Rockets to send a pick or the rights to player along in the bargain, for example a future 1st, multiple 2nds, or the rights to Clint Capela (pick #25 in last month’s draft).
It’s worth noting, the Celtics also have a limited window to use Keith Bogans’ $5 million contract before the deadline to waive him comes up. Bogans’ contract will work in much the same fashion as the TPE because his salary for next season is fully non-guaranteed. Bogans, however, can be traded for multiple players as long as the salaries match.