Respectively is used to indicate order, like if you said "Michael Phelps and Michael Jordan excelled in swimming and basketball, respectively."
You can think of respectively as a word that lines things up in order so they match. You might say that pizza and meatloaf are your favorite and least favorite foods, respectively. If you and your sister were voted Most Improved and MVP in a baseball league, respectively, then you got better and your sister was the best. This word doesn't have much to do with respect, but it is respectful to write clearly, and respectively helps with that.