What does it mean that the FBI got a search warrant?

It means that a federal magistrate judge looked at the information investigators had already gathered and agreed that Cohen probably possessed additional evidence of a federal crime.

Notably, investigators also could have used a grand jury subpoena to order Cohen to turn over the materials they were pursuing, without seeking a judge’s permission. A subpoena would have permitted Cohen to decide for himself which of his files to turn over and which to withhold as irrelevant or falling within a valid claim of lawyer-client privilege. By contrast, when law enforcement officials execute a search warrant, the government goes in and seizes a broader set of materials — like hard drives and the contents of filing cabinets — then sorts through them itself.

Although it is unusual for the Justice Department to seek a lawyer’s materials, the U.S. attorneys’ manual contains procedures for how to get both subpoenas and search warrants in such cases. It tells investigators to exhaust all other ways of obtaining evidence first “to avoid impinging on valid attorney-client relationships.” It also encourages them to use a subpoena if possible. But it also acknowledges that sometimes a search warrant may be justified, even though it is more intrusive, such as if there is reason to believe the recipient would destroy the evidence rather than turn it over.