Silence Dogood was the name Franklin used to write the letters. In the 18th century many people wrote using pseudonyms (fake names used in writing). Franklin made up a whole character who went by the name Silence Dogood and wrote the letters as though he were she.
Dogood claimed to be a middle-aged widow with some funny and intelligent things to say. People suspected that Dogood was not who she said she was, but many were surprised to find out that young Franklin had written the letters.
Franklin's most famous pseudonym (pronounced SOO-Doe-Nim) was Richard Saunders, also known as Poor Richard of Poor Richard's Almanac. Have you ever used an almanac?