A personal website is all about promoting you. You are a brand and your name is the brand name. No one is going to know about your brand unless you get it out there. You need a personal website for number of reasons. You need a website to showcase your work and allow people to contact you.
If you are a business owner or management person then a website helps to brand you. If you re unemployed or a job change, then you d need one to show your prospective employers how good you are and what you can do, so that they might hire you. If you re a blogger or writer, then you might use one to blog about your design life, show people what you re doing and build your online presence.