I will add gogibogi4's correct answer. The Grafana documentation is lacking on this.
In your drill-down dashboard, add a constant variable. To be retrieved in Grafana, you need the prefix var- then the name of the variable in the query string. Let's assume the variable is "region." The URL coming into the drilldown dashboard should look similar to the following:
/drilldowndashboard/?var-region=NorthWest
Drilldown Dashboard Settings:
In the drilldown dashboard settings, create a variable. The Name in this example is "region" Make the type Constant. Under Hide, you can just leave that unselected. Under Constant options, you can write the word "blank" The preview of values will just show the word "blank" but go ahead and save it as it will be replaced in the query.
Query:
You can refer to the variable using [[region]] in your data query.
Parent Dashboard:
The parent dashboard merely needs to refer to the drilldown dashboard with var-region as a query parameter.