Often, Horizontal is explained as 4 cutters working as two pairs of "pistons" going in and out, but the problem is that that's very easy to defend against.
If 4 and 5 are "pistoning" together, and their checks follow, then when they go to reverse directions within the lane...
... smart defenders can switch off to save energy and shut down both lanes.
Notice that Red 4 and Red 5 are running less than the Blue team, by switching checks.
No space has been created.
To create space, the two cutters on the OPEN side of the field (i.e. on the Away side when the force is Away) cut under (inward) and to the BREAK SIDE. This draws their defenders out of the lane.
Notice how a lane is now clear of defenders on the open side of the field. This is an easy throw, to Blue 6, who just has to beat their defender (easy with good cutting).
From here on out it's just standard "Continuation Passes"
Continuation or Flow is the bread and butter of ultimate. This is how games are won or lost.
Let's review. It works the same on the other side of the field.
The two cutters on the OPEN side of the field cut under, and to the BREAK side, in anticipation of the swing. The player on the far side is just jogging upfield. The player in the number 5 position knows it's his/her turn to get the disc and sets up a cut.
The person in the #4 position is there for Continuation passes.
There's no magic here. Just cutting into open space.
Let's look at it one more time, on the Flick side for a righty, with defenders.
Middle handler starts.
Notice again the open late for cutters.
If the long throw is there we absolutely want to take it.
Woo hoo!