Before you begin building your site, you should think about what you want to make available on it. If an employer already has your resume in hand, it doesn't make sense to merely copy and paste this information onto a web site (although much of this information should be available on your site, and you can certainly link to your resume if you wish, or link to a LinkedIn account where this info is available). While a resume may be limited in length or by standardized sections, you'll have a lot of freedom in how you organize and what you place on your professional website. According to Forbes magazine contributor Brent Dykes, you can generate a lot of value by drawing connections among the data, visuals, and narrative you present in something like a personal website.
You may have already collected some of the data you want to share with employers by creating your resume, but a professional website allows you to expand upon this information, providing context and rich media to make this information more engaging to tell a more complete story about who you are. Activities that are just named on a single line on your resume could be developed on your website into a section that reflects on your experience and shares images or video of the event. This can help potential employers visualize what you did, as well as allow you to reflect upon the role of these experiences in your professional development, who you are, and what you value. The internet is a visual media, so it makes sense to try and incorporate images or video to go along with the textual content you create.
All of these add up to convey a narrative--a brand if you will--that communicates who you are, what you hope to accomplish, and what kind of employee you will be. The change referenced in the image that you're hoping for is to change the reader's mind about interviewing you; how you accomplish this is by presenting an engaging site that explains and enlightens your audience. Another way to think about the role of your web site is that it elaborates upon your resume in the same way that you might discuss your professional experiences when at an in-person job interview. You can tell a story that cannot always be conveyed in the basic resume format.