Firstly, a logo promotes your business in the market. A logo gives a unique identity to your business, especially in a website design. The best logo designs are so unique and easily recognisable that the name of the business springs to mind even when displayed with out text. They act as ways of establishing credibility with your customers and building a brand identity.
Therefore, good logo in a web design needs to be memorable. Your customers need to be able to picture your logo easily when thinking about your company. It needs to spring to mind. By the same token, the logo design needs to be easily describable. When your customer is talking about your business with someone else they need to be able to refer to you business in an identifiable way. “That plumbing company with the blue squiggle” isn’t going to cut it.
“That plumbing company with the blue squiggle like water dripping out a pipe” might.
Continuing to use this hypothetical plumbing company logo as an example, the logo needs to be easily scalable. How good will that squiggle look as a favicon in the address bar of a web browser, or on the side of a biro? How good will the logo look on the main page of the plumber’s website, or on the side of his van?
The logo also needs to work in black and white. Will that blue squiggle be distinctive enough if the customer prints off something from the website in black and white?
Having a really good logo makes putting together a website for a business really easy, as the colour scheme and design elements of a good logo can be used as the basis for the whole site design.