The Token Manager is a tool that allows you to store Facebook Page's access tokens (those tokens are needed for the Facebook API requests to get the Page's data/posts/photos/videos...) for the use in the widgets.
The Token Manager works like this: when you click on the "Add New (or update) Token" button, the popup window appears with the Facebook connection process. During this process you choose what Facebook Pages do you want to have access tokens to be stored in the Token Manager. Once you finish this process, the provided tokens will be stored in the Token Manager. You can login to another Facebook account and follow the same process to have other Facebook Pages tokens stored in your Token Manager.
When you create a new Facebook Feed Pro widget, you can use the Token Manager to get the Facebook Page access token.
If for some reason the Page's access token becomes invalid (access token is revoked by Page's owner or the owner changed it's Facebook password, etc.,) you can just refresh the token by clicking "Add New (or update) Token" button and follow the connection process. The existing tokens will be updated and the tokens that were not stored in the Token Manager will be added.
When you delete a token from the Token Manager, this Facebook Page data won't be available in the widgets, that you connected using this token. There is no big need to delete tokens from the Token Manager, so please delete it only if you haven't used it in any widget and will never need it.