It's basically just chaining together portals to move quickly. Effectively line-of-sight teleportation.

Place portal A next to you, then place portal B somewhere else. Step through to location B, then replace portal A with portal C in a new location. Rinse and repeat.

Triple portal is a bit of a misnomer, it's more like walking a pair of portals around. You go through to a new portal, then move the old one somewhere new. It's just like walking, except your feet are portals and you can move them almost instantly.