The following text is taken verbatim from the book, 300 Days of Better Writing: A daily handbook for improving your writing written by David Bowman (2010)
“An introductory adverbial phrase is a phrase at the beginning of the sentence that tells something about the main verb, such as when it occurred, how, or to what degree. Consider this sentence.
“After reading the newspaper, John felt relaxed.”
The phrase “after reading the newspaper” tells when John felt relaxed. This phrase is an introductory adverbial phrase. It is at the beginning of the sentence, and it tells something about the main verb: “felt.” Here’s another example.
“Yesterday, he visited his mother.”
In this example, the word “Yesterday” serves as an introductory adverbial phrase telling about the action “visited.” As such, it is followed by a comma.”