Why does the F.B.I. care if there is classified information in the emails?

Under federal law, mishandling national security information is a crime, one that the F.B.I. is responsible for investigating. In 2015, the bureau began investigating the personal email account that Mrs. Clinton had used exclusively as secretary of state. As part of that investigation, the bureau tried to find every electronic device — phones, tablets, computers — that Mrs. Clinton and her aides used.

Agents could not find many of them, including several of Mrs. Clinton’s cellphones and two iPads. The agents knew that those devices, and others they were not aware of, might someday surface. But they completed the Clinton case because they found no evidence that anyone had intentionally broken the law.

The newly discovered emails may — or may not — provide new information to the F.B.I.

Why did Mr. Comey send the letter?

In July, Mr. Comey told Congress that the Clinton investigation was complete but that if new information came to light, the bureau would examine it. Mr. Comey pledged to be as transparent as he could with Congress about the investigation, and has since made public hundreds of pages of documents related to the inquiry.

According to senior F.B.I. officials, Mr. Comey felt that he would be breaking his pledge of transparency to Congress if he did not reveal the new information from the Weiner case. And he believed that the bureau would be accused of suppressing details to benefit Mrs. Clinton — an accusation that he believed could do lasting damage to the F.B.I.’s credibility.

Who is upset with Mr. Comey for sending the letter?

Many Democrats and even some Republicans have called the letter vague, troubling and unprecedented. Senior officials at the Justice Department urged Mr. Comey not to send the letter, saying it violated the spirit of longstanding policies not to discuss current investigations or do anything that could be seen as meddling in an election.

In the letter, Mr. Comey said that the F.B.I. had yet to determine whether “this material may be significant,” and that he could not predict how long the review would take. Mrs. Clinton’s campaign has pushed Mr. Comey to release more information about the emails.