Here are some reasons why monitoring of backlinks is important;
Quality of the links is important: As earlier said, the quality and not the quantity of the links are important. Sites that link towards your site should be related in some way or the other. When the content or business does not match the content on your site, it becomes unworthy.
Spam Links: When inward pointing links are from spam sites or have questionable credence, search engine bots are more than likely to pull down your rankings.
Reciprocal Sites: This was once very popular, wherein web owners sent request to link their site in return for a link to your site. This is not accepted today and web owners would rather prefer one way links instead of these two way links.
Monitoring all of these helps you to keep your site clean and at harms site. This is where backlink monitoring services from SEO companies come in handy.