The bi-annual exception is another piece of the Collective Bargaining Agreement which allows teams to spend money on salary without counting it against their salary cap. This exception allows teams to spend $1.672M over two years. It can be spent on multiple players if the team so desires.
This particular exception was used by a lot of luxury tax paying teams prior to the new CBA being ratified. For example, the Los Angeles Lakers signed Karl Malone using the bi-annual exception prior to the 2003-04 season. Under the current CBA, luxury tax teams are forbidden from using the bi-annual exception. This was done because teams under the cap did not like that luxury tax paying teams were using the bi-annual exception to sign marquee free agents. Under the current agreement, raises on bi-annual exception contracts are limited to 8% per year. Only teams who are not paying luxury taxes are allowed to use the bi-annual exception.