It depends on what type of backlink it is.
If the backlink is from a high authority website and is relevant to your own, then they can make a massive positive difference and really increase your search engine exposure.
In contrast, if the backlink is from low quality website, or from a spam blog comment, for example, then your website could fall down the rankings, be subject to a Google penalty, or even be removed from Google’s index completely. Thankfully, if you do have a spammer building lots of low quality links, or you’ve built them yourself in the past, you should have the opportunity to deal with them before Google takes action.