Dumbledore orders Snape to rejoin Voldemort, in order to act as a double agent for the Order. He recognises that Snape will declare that he is loyal to Voldemort.
Snape tells Bellatrix (and Voldemort) that he is loyal to the Death Eaters and acting as a double agent for them; he explains that he can get away to meet with them because Dumbledore believes that he (Snape) is acting on behalf of the order.
Both sides believe Snape is working for them, while pretending to act for the other side.
As FreeMan points out in the comments, this also (out of universe) creates ambiguity for the reader by keeping it unclear where his true loyalties sit.