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It's the invisible line you follow through a curve isn't it? That's the definition I've gathered from various contexts.

If so, what is an early apex? Late apex?

The easiest way to explain it is to imagine a ball thrown upwards. Not straight up mind you. It follows a smooth curve if you were to track it's path. The Apex is the very top point.

In a turn it's the same idea, the highest part, or the furthest point from the start.

I think....

from what i understand...

using a delayed apex in a corner leaves you w/ more room to adjust midway in the corner (in case of road hazards) and have a better exit line. therefore, you're able to accelerate earlier and be faster in the corner.

This explains it:

http://www.turnfast.com/tech_driving/dr ... ring.shtml

Here is an illustration to show it:

As we can see, the apex is the mid-point of the corner. Of course, this illustration doesn't necessarily represent the best cornering line approach for bikes. As VX touched on, and according to my own reading, the 'delayed apex' is the technique to use. You 'turn in' later, see farther through the corner as a result, and have much less probability of exiting wide.

delayed apex is the safe way on the street.

The illustration shows the fastest possible line for anything that would take that corner. THOUGH depending on the NEXT turn after that, you'll tweak the line so you can get a decently fast line through both/all turns.