When things work correctly, it matters. Right now lemmy's sorting system is bugged, so just using "new" is the best way to find content.
But, when it works, the upvotes and downvotes determine how much visibility a post is given. It's basically a way for us users to tell the site what content is good, and what content is bad. If you see a thread with interesting discussion, or that links a fun video, or features a pretty art piece, upvoting will help more people find it.
If you see someone link to misinformation, or push a conspiracy theory, you can downvote to the tell the system that it is bad content, and it will show it to less people going forward.