Your question is about the lifecycle of objects in between requests. It's important to understand that webapplications are used over the HTTP(S) protocol which is a stateless protocol. This means that every request is a completely new request for the webserver and there's no state shared between requests.
However it would be foolish to send the credentials of a user to the server each and every time so a webserver can create a thing they call a Session (and session-state). This object is an object that remains available for the lifetime of the session of the current user (most of the times from logging in until logging out). You can use this object to store items that you wish to share over various requests of the same user.
If the values you're trying to keep are specific to the page you can probably use a hidden field or something like that. However if the data is more related to the user than to a specific page and it must have a lifecycle longer than a single request then sessionstate is the best place to store the data.