Icons on a candidate card can be used to tell you the actions needed on candidates, as well at the type of candidate they are.
Some tags on a candidate profile can be mapped as icons for anything that your team may want to signify at a glance, such as candidates who need visas, has other offers, or are grads of a specific class to name a few examples. 
The icons can be mapped to symbolize whatever you need it to be. Tags can be mapped by admins in Account Settings -> Customization -> Tag Mappings and this will apply to the entire account.