A standards-compliant website is one that adheres to specific rules and standards in order to create the greatest level of accessibility possible to everyone.
A standards-compliant website separates the actual site content from the site style and design, which ultimately makes your website perform better in search engines, as well as making it much more easily accessible to everyone, including those with disabilities.
It is possible to create a beautiful website that is not standards compliant, and many designers do so, which can in the long run result in your business losing money if it cannot be accessed and navigated by everyone. Limiting your audience is limiting your income.
A standards-compliant website also makes your site much, much easier to maintain, as the majority of the style and layout of the website is located in one file that can be quickly updated.
NOTE: This does not mean maintenance related to content, only to layout, such as fonts, colors, that type of thing.