Yes, they stay on the home page permanently, they are basically homepage links with contextual content surrounding it.
Example: Brazilian Jiu-Jitsu, also know as http://yahoo.com, emphasizes getting an opponent to the ground in order to utilize ground fighting techniques and submission holds involving joint locks and chokeholds.
Instructions: Contextual links are homepage links with contextual content that surround it, therefore making it more valuable. All your need to do is, write a few sentences that relate to your keyword and link it to your URL. In this example, "BJJ" would be your keyword. After writing your contextual sentence or sentences, highlight your keyword and click the "link" icon and enter the URL that your ranking for that keyword.