It allows you to learn things quickly and switch things up when needed. It is a very important skill to have simply because work environments are constantly changing. Your ability to respond effectively determines where you stand in the company. If you can't adapt, you could be left behind, or even worse, you could be seen as a bad fit for the company.
One way to learn or improve your adaptability skills is to change the way you think. Change is a scary thing, but it's not always bad. Look at it as a chance for you to learn new things and improve. This extends to the way you view opinions or perspectives of others. Switching up your thought process opens the possibility to practise what you already know and also try new ways to do things.
A key part to being adaptable is taking risks – it can be something small at first like proposing an idea at a meeting, and could gradually increase with the risks you take. Remember though, with risks comes failure and that's just part of learning.
Surrounding yourself with people who are like minded helps the development of this skill tremendously. If you're stuck with people who refuse to adapt you'll be tempted to do the same. Try and get them to be open as this eases the load and makes it a much easier journey.
Learning this skill isn't the hard part, putting into practise is. But the more you do it the better at it you get.
Work environments are always changing and you need to keep up
Change the way you think
Learn to take risks
Encourage those around you to adapt as well