Very much; by a very large amount. It is a strong word for size of difference, and this is the key to using it: 'vastly' almost always sits next to something that already means change, difference, or comparison. So you get 'vastly improved', 'vastly different', 'vastly increased', 'vastly outnumbered', 'vastly better', 'vastly more expensive', 'vastly overrated'. English speakers do not usually say 'vastly happy' or 'vastly tired', even though those are also 'very' — with a plain adjective we say 'extremely'. There is an older, more literary use meaning simply 'extremely' ('I am vastly pleased'), which you meet in old novels and which now sounds either very posh or joking. In normal modern use it is a formal-ish written word: news reports, business writing, essays. In conversation people say 'way better', 'a lot more', 'totally different'. Its power comes from the picture inside it — 'vast' means huge like an ocean or a desert — so save it for gaps that really are enormous, or it loses its force.