I believe this question has been answered elsewhere, but to summarize:
a) this is a configurable setting - in the Application Administration area, you can set it so the service field is not required.
b) if you want to use it - which we recommend using it - the field links to the "Business Service" class of the CMDB. Any Business Service CIs that are linked to the user (customer for the ticket), the user's organization, or the user's company with a "Used By" relationship will show up in that list.
Hope this helps!
If you are not using the Remedy CMBD/Asset management module, then you can goto Application Administration > Custom > Incident > Advanced options and make this field non-mandatory.
If you are using the Remedy Asset Management module then you will need to configure the asset/CI and relate it to people. So that it will appear in the Service CI field.