The line pressure cable controls the fluid pressure out of the transmission pump. That pressure is used to actuate the various clutches and bands, as well as push fluid around to lubricate and cool the various parts.
The more power you are putting through the transmission, the tighter you need to clamp the clutches, so you need more fluid pressure. During high power shifts you also need to shift faster to prevent something called "shift flare", where the engine speeds up between shifts roasting the clutches.
At lower speeds you want less pressure to soften the shifts and to reduce noise, pump losses, wear, and temperature rise. With the engine idling, pull the cable out and you'll hear and feel what I am talking about.
Since you have it disconnected, you can pull the cable fully out and fix it in place temporarily using a zip-tie. Go for a drive and you'll notice much harsher shifts at low speeds.