Without resorting to drawings, electrical theory, or links to other sites, let me try to explain. I will leave out the high-leg Delta for a moment. Delta and Y describe the physical (and electrical) way the wires are interconnected.
Three phase power comes from three transformer secondaries, each with two wires, one at each end of the winding. Let's call the windings A, B, and C, and tag the ends of A's winding A' and A", B's winding ends B' and B", etc.
In a Delta system, the wires are connected so a triangle (a.k.a. a delta) is formed, with A" connected to B', B" connected to C', and C" connected to A'. Now, we connect each junction to a wire. Let's call the A"-to-B' junction A-B, and so forth.
Now, we have three wires: A-B, B-C, and C-A (usually called A-C). These are our phase (i.e., hot) wires, and the voltage between any two wires (a.k.a. line-to-line voltage) is the same as the secondary voltage of each transformer.
Notice that we have not grounded any of these wires (yet; we'll get back to that in a bit.) Because of that, there is no real voltage from any phase wire to ground (again: yet). This is what is known as an ungrounded service.
Now, a Y-system has the same three secondaries, but interconnected differently: A', B', and C' are connected together, and A", B", and C", are the phase wires. If you spread the windings out radially, they form a Y pattern, like a Mercedes star.
Usually (almost always, actually), the center point of this Y is grounded, and called the neutral. The voltage from any phase to ground is equal to the secondary voltage of each transformer, but the line-to-line voltage is 1.73 times (not twice) the line-to-ground voltage.
This is where the 208/120v Y system comes from. There is 120v from any phase to ground (neutral) with each winding at 120v, but 208v (120 x 1.73) between phases. The 480/277v Y system is connected the same way: 480v line-to-line and 277v line-to-ground.
Now, back to our as-of-yet ungrounded Delta system for a moment. There are two ways of grounding a Delta system. The simpler way is to simply ground one of the phases, which then creates what is called (oddly enough) a corner-grounded Delta system.
You should be familair with the typical 240/120v 1-ph system, like you likely have in your house, where a single transformer secondary winding has a center tap, which is the grounded neutral. The line-to-line voltage is 240, and the line-to-neutral voltage is 120.
Remember the A, B, and C labels given the Delta-system's three transformer secondary windings? Let's say the transformer with the grounded center tap is C, with the two phase wires flanking it A-C and B-C. There will be 120v from A-C and B-C to ground, and 240v between any two phase wires.
However, something strange happens to the voltage between phase wire A-B and ground. The voltage at this point is higher than 120 to ground, because it comes from the voltage across both the A winding (or the B winding) and half of the C winding, and is called the 'high leg'.
This condfiguration is sometimes called a center-tapped Delta, sometimes a high-leg Delta, both of which are fairly accurate descriptions. By the way, you should never attemp to power a load between the high leg and the grounded neutral.
The center-tapped winding of the Delta system is exactly, and I mean exactly, the same thing as the residential single-phase system described above, as far as the A-C and B-C phase wires are concerned: 240v line-to-line, and 120v line-to-neutral.
The only difference is that you have a third phase wire with an unusable higher voltage to ground, but a very usable and symmetrical 3-phase line-to-line voltage (240v), which ignores the line-to-ground voltage for 3-phase line-to-line loads.
Lastly, the Y system is best when there are mostly line-to-neutral loads, and the Delta is best with line-to-line loads, but both systems can supply both types of loads, and even at the same time. The high-leg Delta is best with large 240/120v loads and a small 3-ph load.
Okay, I'm plumb tuckered out. I hope this is helpful.
