"The Archon Toilet refers to a Protoss tactic unique to Wings of Liberty that combines the Mothership's Vortex ability with the Archon's high splash damage output to destroy large groups of enemy units quickly."
It's a "Black hole" that temporarily sucks the enemy's units in. Players quickly learned they can send in their units along with the enemies. So the trick is you send in a unit called the Archon which does splash damage. The split second that the black hole ends all the units emerge at the same time in a super concentrated area, so the Archon's slash damage hits all the enemy's units at once.
The big ship on the right casts a black hole and sucks the other air ships into it. These are strong units and normally are pretty spaced out so they are safe from splash damage. The black hole however spits everyone back out in the exact same spot so they are momentarily clumped together. So to take advantage of this you have those big blue balls of energy called archons. They have short range, lots of damage, lots of splash, not so good hp/shield so they are kinda of squishy. But if you throw them into the black hole too then they can come out at the same time as the enemies and blow shit up (since clumped enemies + your units in range with lots of splash)