IMO, the term "double apex" is a bit of a misnomer. Here's why.
It's usually used for a long turn, which is treated as two turns -
not in terms of apexes, but in terms of positioning the car. I'll use the line through turn 4 at Willow above as an example. Coming out of turn 3, you pass one "apex" when you come near the right edge of the pavement, and you track out to the left side. At the left edge of the pavement, you reach the sharpest part of the turn (smallest turning radius). After getting the car rotated is the second turn, in which you pass the second "apex" at the right edge of the pavement before tracking out to the left for the entrance to turn 5. Two turns, each with an "apex" on the right - hence the term "double apex".
However, this assumes the word "apex" is defined as the point at which you reach the edge of the pavement on the opposite side from where you enter the turn and exit the turn. The word "apex" can also be defined as the part of the turn that has the smallest turning radius (sharpest part of the turn), which means that it is the slowest point in the turn. Under this alternative definition, it's clear that this is actually a turn with only one apex, one point at which the turn is slowest, before which you brake, and from which you can accelerate out.
For another example of a turn which is often taken with a "double apex" - meaning, where you are at the opposite edge of the pavement - look at turn 8 at Putnam Park:
As you can see from the diagram, it's a 180 degree turn with a relatively constant radius. Some folks take it as a constant radius turn, while others use a "double apex" with a distinctly sharper point where they rotate the car midway through the turn, in order to straighten out (and quicken) the approach to that point and the exit from that point, as Bob mentions.
Hope that makes sense.