Also known as citations or local listings, directories can vary quite widely, but the core of what a directory is, is basically a digital version of something like Yellow Pages where people can visit to find a list of businesses that provide a service they are requiring.
Most business directories offer a range of options, some have free and paid tiers for premium features - such as a more prominent placement on the website, or additional options to add to your directory listing.
Most will allow you to create an account and add your business to the directory, including things like your business name, website, address, phone number, logo, business hours etc.
In a lot of different industries, there are also directory websites built specifically for that category of business. You can also get directories that only accept businesses operating within a specific area.
Citation building is still quite an important part of a
local SEO campaign - Yes, even in 2020. They help to establish a good online presence and provide Google with trusted sources of information about your business. Building a good list of local citations for your website can be a great way to get some quick wins and see some movement with your rankings in Google.
Google uses local directory websites to help verify your business information such as the business name, address, phone number, and website. Having up to date, accurate, and consistent information about your business listed across the web is what most professional companies do, so if you can replicate the strategy for yourself then you are more likely to be viewed as an authoritative and trusted site by Google.
Not having this information around the web puts you at a disadvantage, because all of your competitors will be doing some kind of citation building. It is in your best interest to do what you can to out-compete other websites by building more citations and doing a better job at ensuring they are consistent, detailed, and accurate.