Think of your domain name as the address for your website. Much like your home or business needs a unique address, so does your website.
The internet is full of places such as Facebook and Etsy that have made it possible to have an online presence without a domain name. Although if your aim is to build your brand and be widely visible, it would be in your benefit to have your very own domain name. Your domain name can speak volumes about your business. Your own domain name will let your potential customers and clients know that you are indeed a legitimate business that has long term plans.
The cost of a domain depends on the domain extension (the part to the right of the dot e.g. .com, .net or .pizza). Some domains can be registered for under $10/year, while others are more expensive.