Even if you have a Facebook page for your brand or business to attract and update fans and customers, you still need your own home on the Web, if for no other reason than to appear to be a legitimate entity. It's never been easier to set up a professional-looking, design-forward website. Well-known site builders like Squarespace, Weebly, and Wix are constantly improving, and they have lots of company, with more competitors arriving all the time with their own new clever twists.
But let's talk a little more about why you even need a webpage in this day of social media domination of the web. On a personal level, you probably wouldn't want to send prospective employers your Facebook page, so a personal website makes sense as an online, custom resume. Another reason worth consideration for both personal and business sites is that building your own gives you far more design choices. You also get a lot more control over products and services you may sell. Furthermore, having a real, dedicated site makes your business seem more authoritative and trustworthy than Facebook or Tumblr on their own (though you should certainly also consider them as elements of your online presence).
Getting your own website used to require a lot of tech wizardry such as knowledge of servers, HTML, site registrars, and Web hosting services, but thankfully, we live in the age of easy online site builders.