Why is it so important to update the content on the business website?

Well for starters, a fresh website is one that customers trust. It shows the business is engaged online and that the information is fresh. For example a coffee shop that updates it's offers every day, a bit like a traditional chalkboard, is more likely to draw customers more regularly because they have interesting offers.
And that's not all. Even search engines which crawl websites give sites which are updated regularly with relevant data more importance when it comes to search queries and results.