There are a lot of tools, free and premium, that can show you the backlinks. Ahrefs, Moz to name two of the most appreciated tools. You can also see links to your website in the dedicated section in Google Search Console. It’s free and it’s from Google so you can perceive it as first-hand. Still there are some things to consider if you go with Search Console to monitor your backlinks.
Normally your ranking on Google is based on the links pointing to your website and discovered by the Google bots and indexed in the link graph (we’re talking about your website’s popularity and authority here, there are way more ranking factors involved). But you probably won’t see all those links in Search Console, Google doesn’t have some strict guidelines on what’s shown in that report. You can see it more as a sample of links pointing to your website. If you have a small website, it may cover most of the links, if you have a larger website you have to know Google has a limited storage available for these links within Search Console so at some point it becomes inevitable the links get cut off and Google tries to show you those links he considers they are more relevant to you as webmaster. Plus, Google doesn’t take out links that are nofollow and doesn’t take out links that are in the disavow file so they might eat up the space for more valuable links.