In drupal 7, for field widget type, what is "server side" used for?
I can't find any reference on Google to a widget that provides this type of functionality so I can only assume it's something custom, but I think the reasoning for it would be the same regardless:

When using the Drupal form API you can add an element of type value which keeps that element server-side only...i.e. the value is available to the form submission/validation functions but it not exposed to the user. A hidden field would still be exposed in the form's HTML so could theoretically be changed by the user before the form is submitted.

I would guess in this case it applies to the node edit form, each node would essentially have a non-editable field with a constant value. I'm not actually sure how useful this would be in normal life but I guess if every node had to have, for example, a geo-location map associated with it, and the value of that location field had to remain constant, this would do it. The same map would just be outputted on each node.

To be honest that could all be nonsense though, it's just an educated guess :)