In order to publish an ArcGIS Server service, you need to author a resource (a map document, for example) that would contain some data which can be local (that is, stored on the same machine where you have your ArcGIS Server installed) or stored at a shared location (such a shared folder). What you need to do then is to make sure ArcGIS Server ArcGIS Server specifically ArcGISSOC account has access to the resources you are trying to publish.
Here is the Tutorial: Publishing a map service
When the service will be published, the client sends request to the ArcGIS Server (server1). The SOM (think manager) component asks SOC (think workhorse) to get the data needed. The SOC process (run by ArcGISSOC OS account will go to the server2 and get the file geodatabase data provided that it has file and share permissions applied). The composed data will be compiled as a raster image (in case of map service) or as a raw data (geodata service) and sent to the client side.
Read more about Preparing resources for publishing as services
PS. In case you will get a chance to upgrade, switch to 10.1/10.2 which have a more robust architecture and provides a better server platform comparing to 10.0. Esri will retire 10.0 in the upcoming years, too, so don't spend too much time learning outdated technology (unless really needed).