While it may be obvious that the background makes a difference in a photo, this is an area that truly separates a lot of pros from amateurs. The professional sees the entire photo and arranges the subject to have a good relationship to the background. Sometimes, all you have to do is take a step to the left or right.
For this sequence I circled Nicole taking her portrait against a variety of backgrounds at a point of land on a lake at a state park. It was generally overcast for this sequence: I could not have done this sequence on a sunny day because the changing quality of light as I walked around Nicole would have been much more noticeable than the background changing.
Bottom Line: See the whole photo and arrange your subject to work well with the background.
(roughly) 105mm, 5.6, 1/250, ISO 400