in the API application form you get a client ID and a client secret, you must use those in the settings. They are used to identify your website/application.
then you need a OAuth token that is what the API is returning to the application once the LinkedIn user has given access to his profile to your website. The token is something that says “this website as access to that guy’s profile”
when that token is invalid (can be several reasons, one them is that you don’t have one) or expired (they expire after 60 days) there is a message at the top of the dashboard that says so and provides a link to the LinkedIn API (a complex request) to ask for a token. You can also use the big blue button in the settings page to ask for a token.
When you click that link, what happens depends on whether you are already logged on LinkedIn or not and whether you already gave the authorization for that website to access your profile or not.
If you’re not logged in and never gave the authorization then LinkedIn will ask you to enter your username and password (plus, may be, other things if you have multi factor athentication activated) then they will ask you if you authorize the application to access your data.
Actually, it works exactly like when you start playing Candy Crush Saga or Holdem Poker on Facebook (except you’re probably already logged in Facebook so they don’t ask you again)