An upturn is a rise or improvement, especially in business, the economy, or how much of something is being sold or done. Like upswing, it carries the picture of a line on a graph that was flat or falling and has now turned upward — the turn is the key part. So an upturn is usually a change for the better after a difficult stretch: 'an upturn in the economy', 'an upturn in profits', 'an upturn in tourist numbers'. Its opposite, downturn, is very common indeed — 'the economic downturn' is the normal polite way to say a bad time for business. The usual pattern is 'an upturn in + noun', and often 'a sharp upturn', 'a slight upturn', 'a modest upturn'. There is also a verb, to upturn, but it is rare and quite formal, meaning to turn something over or upside down; you are far more likely to meet the adjective upturned — an upturned box, an upturned boat, an upturned face looking at the sky. So keep the two apart: the noun upturn is about numbers going up; upturned is about physical things turned over. In business news you will meet upturn and upswing used almost the same way, though upturn is the more common of the two.