It just means get down to what ever alt. they assigned by the time you cross the intersection or VOR metioned, that's all. It's not a big secret. Figure out how far you are from the fix and decide when you need to decend then decend. That's it... ;-)

Exactly, no secret. I'm sure this has been said before but I dont have time to read all these posts. So here's my 2 cents. There is basically a couple reasons for this clearence, this is what I was taught and what i read. There is, of course, a transition altitude between Center and Approach. Here at chicago it is 13,000 feet. So when we say: xxx, radar contact. Continue on the XXX.X arrival. Cross X at 11,000 feet ( different in other ARTCCs) and 250 knots IAS. Decend at pilots discretion. We want you on that altitude for proper handoff so approach or any other TRACON can handle you. Now, if there is alot of traffic, the reason would be for proper flow and separation and a nice smooth handoff. This is all probably wrong but hey, thats what i am contributing to this. Bye ByeBenjie