The word importantly emphasizes something. It’s often used to call attention to something in a list, and most importantly, it comes from the word "important."
Indeed, importantly comes from the word important, which has roots in the Latin word for “being significant.” When you see the word importantly, you know something significant is being mentioned or emphasized. If your boss gives you a bunch of jobs, then says, "Most importantly, be careful with the Penske file," then that file is your priority. It often appears as most importantly to give it a little extra oomph.