Here's an attempt at a simpler explanation:
Django is pronounced with an initial sound that, in English is often written "j". This might lead one to think of the "D" as silent with the "j" being pronounced the way it is in English.
However, that doesn't explain why the "D" is there in the first place.
A more insightful way to think of it is to remember it's a French spelling. Think of the "j" as being pronounced as in French. Now put a "d" sound in front of it. When the "d" sound and "j" sound merge, you get something called an affricate. This particular affricate is the same sound used in English to pronounce just "j".
So a French "dj" is like an English "j". The "d" isn't silent, though, because the French "j" is not the same as the English "j".