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.
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.