When it comes to your websites design - appealing to your target market takes top priority - most people are heavily swayed by the appearance of your website, it could determine whether or not they choose to trust your brand.
It's important that you keep your websites design up to date - those who are very familiar with facebook will take notice that they make small and sometimes large changes to their website very regularly, they are always doing research on how to appeal to their user base to achieve their goals at hand. You would also notice some other brands have changed their websites and continually make gradual changes. This keeps the user from seeing the design of the website as being dated and lacking upkeep. It shows the user that the brand is invested in their development.
You'll notice that other popular websites haven't changed their websites in years - why not?
Well they make take preference to follow the if it's not broke, don't fix it mentality. But even they too eventually have to make the switch as is usually the case.
Instead of a complete redesign of the website - others often opt the simply change the design language.
The most popular design language out right now is Material Design - by Google.
A website inspired by material design.
While not getting into the details, it's what android is currently built with.
Since android is the most popular operating system, wouldn't it be cool if you could let your user experience your website in the same familiar way they do with their phone? wouldn't that be intuitive?
Well that's exactly why there's been an uprise in the sites that use Material Design - not only is it modern, but it's also intuitive and focused on the user experience.
The User Experience of your site is born from the design that you choose for your website - (thus the high costs of web design).
The better looking and the more responsive your site - the higher the chance of you retaining a visitor - and thus your web traffic is likely to increase. Which is the ultimate goal of your website. The more traffic to your cause/organisation the better the results.