What are unnatural links and how to find them?

I’ve been warned about “unnatural links” potentially hurting my site’s SEO, but I’m not sure what qualifies as unnatural. How can I identify these in my backlink profile? Are there any tools you recommend for finding them? And once I do find them, what’s the best way to deal with them? I want to make sure my site isn’t being penalized for links I didn’t even know about!