Your website is the main source of your online business; it is the internet representation of your company whether your company exists physically or not. When you are working on business online, people cannot see you physically like how they could if they were interact with an offline company. Hence, people do judge you by your covers. This is where a good design comes in.
Suppose if you are working an offline company. Would you permit your salespersons to be dressed in shabby or casual clothes when they are dealing with your customers? By creating your staff wear professionally, you are telling your customers that you do care about quality. This works simply because first impressions matter.
Simultaneoulsy, the same case is with your website. If your website is put together shabbily and looks like a 5 minute "quick fix", you are literally shouting to your visitors that you are not professional and you do not care for quality.
On the other side, if you have a totally professionaly develope website layout, you are giving your visitors the perception that you have given meticulous attention to every detail and you care about professionalism. You are organised, focused and you really mean business.
Similarly, you should also have anything related to your company well designed. From business cards to letterheads to promotional brochures, every little bit matters. This is because as you grow your business, these items become the face of your business. Once again, think of the "salesperson dressed shabbily" anology, and you will get my point.