To illustrate this, I setup this destination link, which displays any variables sent to it:
And I created a redirect link to it, http://twe.to/1dc1
If you click either of those links, you will see an empty list, as no variables are attached:
And if you click these versions of the same links with variables attached, you will see the variables listed:
Or the redirect link, http://twe.to/1dc1?hello=happy&goodbye=sad
In both cases, you'll see the same result:
So, back to our campaign example, if your affiliate destination link accepted the variable "cid" for "campaign ID", you could append a different cid value for each advertisement to your tracking link, like http://twe.to/1dc1?cid=1 and http://twe.to/1dc1?cid=2.
This works on keyword links, short links, and domain redirects, however, I only recommend using it in cases where people cannot see the link, like in PPC advertising. If you want to pass variables on keyword links or domain redirects (and it's always the same variable and value), see the tutorial on embedding hidden variables instead of doing it the above way, which makes it look like a tracking link.