Here's a good (over-simplified) example of staging:
Let's say you wanted to find all of the high-risk individuals in your city (Might as well be interesting about it). You have a Phone company dB (national) indexed by state, city, last name, first name, address and an FBI dB (global) indexed by last name, first name, country, region, address. Let's say the FBI dB has multiple records for each individual due to multiple past addresses.
You could join the two dBs on the common elements and then qualify your criteria. Or...
Select RecordID from Phone as P1
Where State = 'MyState' and City = 'MyCity' and
exists (Select 1
From TheMan as M1
Where M1.Last = P1.Last and M1.First = P1.First and M1.Risk > 80)
Now I have a small record-set to qualify and a small result-set to work from. From there I can go get details. That's a good candidate for a CTE and I could shoot a dozen holes in the logic, but it illustrates the concept. If you bring M1.Risk (non-indexed field) into the equation with a full join, you're forcing SQL Server to plan against it in certain situations. Not necessarily here, but as your logic gets more complex and subsequent non-indexed criteria comes into play.