In a household 120/240 system, you have two hot legs and a neutral. The neutral is connected to ground in the breaker panel, and represents the center connection of a center-tapped transformer. Between either hot leg and the neutral, you're making a connection between only "half" of the transformer- so you get 120 volts. Between the two hot legs, you're getting the "whole" transformer, or 240 volts.
Hard to explain a delta vs wye system without drawing a picture, Steve. But I'll try.
Picture yourself in an imaginary circle. You're in the very center, and three people are standing at the edge, equally spaced. You're the neutral. You can shake hands with the three people, alternately. That's WYE.
Now picture three people making up a triangle. They can shake hands only with the person to their left or right. Nobody is in the middle. That's Delta.