My understanding is:
For the cross, the horizontal line serves to indicate your wing angle, while the vertical line above the cross references your lift vector. I believe the theory is it's a quick reference to make sure you're "wings level" to the target when pulling the trigger in a tracking shot.
As far as the ranging hash marks (as seen in the Mk. VIII) the theory is that you can use those to determine how much lead to give the target if you know the:
Bullet Flight Time (determined by bullet velocity + shooter airspeed, range to target)
Target airspeed
Deflection Angle
In the case of the Mk.VIII, each hash mark is at 5mil increments, so you can, in theory, place your sight on the correct hash mark for how much lead you need to give. However the math involved is INCREDIBLY complicated, so you're probably best off shooting from dead reckoning, anyway.
The hash marks below the cross on the Mk.VIII could also be used as an aim point for bombs and rockets. Just as with leading a target, there's some equation of dive angle, relative altitude, speed, etc. that would tell you on which hash to put the target when aiming.
As far as the angled lines on the Mk.VIII (below the cross and at a 45 degree angle) I'm not sure what purpose they was meant to serve, but I find them useful to help estimate my bank angle.
Bore sight is pretty simple. More or less says "Bullets go Here" when shooting a stable or 0 deflection target.