This list is oftentimes referred to as NAP or name, address, phone. These are important listings because they provide important information for Google to analyze. It tells Google that you're actually in business and where you're located within Denver.
And this is why the search engines look for this information before deciding to list your business in the local map packs or what the top listings in the SERPS are typically. Without this information backing up what you've told Google by claiming your Google Local Business listing, you're much less likely to find yourself ranking in the local map pack.
On the other hand, if your local Denver business has this data listed in other places like Yelp, Merchant Circle, CityPages, DexKnows and a host of other websites including Google the likelihood of your business showing up for those performing a search from Denver or a surrounding community are a lot higher. Ideally when someone performs a search from somewhere like Lakewood, Golden, Highlands Ranch, Littleton or other areas and you're located in Denver proper you still want to show up for that search if you're the most relevant company. Having your citations right helps you do just this.
When I say having them right I mean having them on trusted websites and having all of the information actually line up. This means that your business name needs to be the same across each and every website you're listed on along with your address, your phone number and your URL. This is the data that Google is looking for when cross referencing your information. Yes, they are actually compiling a database about your company/website to determine if your data is accurate so that they can rank or not rank your website accordingly.
I've aware that there are hundreds of websites that you can get listed on for a link or local citation. Thing is, they're not all the same. You want to get listed on the power player websites first, the guys like Yelp. Google loves them some Yelp and you should too.