I can only imagine of sending a value from the server to the client which is (unchanged) sent back to maintain a kind of a state.

Precisely. In fact, it's still being used for this purpose today because HTTP as we know it today is still, at least fundamentally, a stateless protocol.

This use case was actually first described in HTML 3.2 (I'm surprised HTML 2.0 didn't include such a description):

These fields should not be rendered and provide a means for servers to store state information with a form. This will be passed back to the server when the form is submitted, using the name/value pair defined by the corresponding attributes. This is a work around for the statelessness of HTTP. Another approach is to use HTTP "Cookies".

<input type=hidden name=customerid value="c2415-345-8563">

While it's worth mentioning that HTML 3.2 became a W3C Recommendation only after JavaScript's initial release, it's safe to assume that hidden fields have pretty much always served the same purpose.