The client ID / Token is defined when using the SOAP API and goes in the CallOption.client. It allows your app to access professional edition orgs via the API. I think Salesforce assigns it to you when you pass certification, but there isn't anything stopping you passing in whatever value you want.
There isn't a direct equivalent for the REST API that will populate the Client Id. Instead you can get you app whitelisted by Salesforce.
If you have a partner app you should now be able to get your OAuth
client whitelisted for api access, talk to your contact in the partner
Source: Does the REST API support Client ID?
The REST API now supports the Call Options Header that can define the
Sforce-Call-Options: client=caseSensitiveToken; defaultNamespace=battle