A LinkedIn badge is one of these buttons here, and when you add the code to your website, this badge or button will show up on your website, and when they click on it, will take you directly to your LinkedIn profile.
The way you access this page is by logging into LinkedIn with your username and password, and then after linkedin.com, go to profile/profile-badges, and that’ll take you this link. You’ll need to pick the appropriate sized badge that you want to include in your website, and then send this content. Copy and paste the content here, send it to your web master.
If you have a WordPress website, you should be able to install a widget, typically in a side bar, and then add this code to that widget in order for the badge to display. Again, if you’re having success with WordPress, give badges a try.