The phrase often implies someone's feelings or thoughts deserve respect and understanding. When she spoke about her dream, her parents took her seriously and supported her.
Pro Tip 2/3
Not a Joke
Using this phrase means the subject is important and should not be laughed at or dismissed. He implored them to take the safety warnings seriously before the storm hit.
Pro Tip 3/3
Authority Recognition
Sometimes it's about acknowledging someone's authority or expertise in a subject. The interns learned quickly to take the supervisor's advice seriously.