"You will have to give Voldemort the correct date of Harry's departure from his aunt and uncle's," said Dumbledore. "Not to do so will raise suspicion, when Voldemort believes you so well informed."
Snape had just killed Dumbledore, why would it raise suspicion about the movements of Harry's departure? it would seem likely that once Dumbledore died at the hands of Snape the Order would surely have changed any plans they would have had in place for Harry's exit from Privet Drive?
In the first chapter of the Deathly Hallows, Snape reveals the date of the move to Voldemort in a meeting of Death Eaters.
"My Lord, the Order of the Phoenix intends to move Harry Potter from his current place of safety on Saturday next, at nightfall."
The interest around the table sharpened palpably. Some stiffened, others fidgeted, all gazing at Snape and Voldemort.
"Saturday . . . at nightfall," repeated Voldemort.
His red eyes fastened upon Snape’s black ones with such intensity that some of the watchers looked away, apparently fearful that they themselves would be scorched by the ferocity of the gaze. Snape, however, looked calmly back into Voldemort’s face and, after a moment or two. Voldemort’s lipless mouth curved into something like a smile.
"Good. Very good. And this information comes—"
"—from the source we discussed," said Snape.
(bolding mine)
It's insinuated that Snape not only was a spy but managed to turn others and had other spies working for him.
This was important as Snape's usefulness might have ceased with Dumbledore's death: Dumbledore wanted to make sure that Snape continued to be deep in Voldemort's plans and favour. This way, Snape would likely become the next Hogwarts Headteacher and protect as best as he could the students of the school as well as pass crucial information to Harry later on.
It seemed to me (and I cannot point to any direct evidence in the text) that Snape broadly hinted that he continued to have a "rat" (not Wormtail) in the Order of the Phoenix: someone who was keeping him informed of the up-to-the-minute activities of the Order.
Dumbledore didn't know exactly how long the Hunt for Horcruxes would take: he had to ensure that Snape would stay close to Voldemort. So he told Snape to build up his importance to the Dark Lord. It underscores the importance of Snape's skill at occlumency. He had to hide this disposition from Voldemort, while appearing to be wide open to him.
