Torque converter

The stall speed refers to the maximum engine speed that can be achieved when raising the speed of the engine with the trans in gear and the brakes locked. It is essentially the amount of slip built into the converter. The idea is the higher the stall speed the more the engine speed can be raised to get more torque applied to increase the speed of take-off from a stop.

This is a pretty good lay mans explanation and I'll only add to it. Since the science of it is way more complicated.

The stall speed refers to the maximum engine speed that can be achieved when raising the speed of the engine with the trans in gear and the brakes locked.

This is mostly correct in a way. The engine speed is raised without a serious engagement or drive of the wheels. Once the converter reaches the stall speed it is rated for, and that is very variable for each converter no matter what they rate it at, the car starts to move . Do note that it can and will move before the stall speed is reached. It just lacks power.

Even with the brakes on, the car can be pushed forward before the rated stall RPM is reached. Though, when it is reached and gone beyond, it's light them up city.

It is essentially the amount of slip built into the converter. The idea is the higher the stall speed the more the engine speed can be raised to get more torque applied to increase the speed of take-off from a stop.

The part in bold. This is a really good description.

The second part is also really good and a basic dead on. Heres the idea in another way to help understand it. Your cam and engine start to make nice power at lets just say.... 2000. The cam operates in the 2-6K range. If you delay the strong engagement of the trans and let it slip a little bit to quickly get to that 2K RPM area, the car doesn't get bogged down with the weak engine torque and bog or stall out. The higher stall allows the engine to get into it's power area and then the converter starts to work.
Your off the line performance increases because of this.

Now lets step it up to a more radical ride. Lets pretend we have a Duster with a very powerful engine and a big cam. This set up doesn't start to work until 4500/4700 RPM. Thats a lot of RPM to wait until you get moving from a dead stop. But since the starting line is where you launch from, you bring the RPM's up past the converters stall, and for Ha-ha's, we'll say it is a 5000 stall, with your trans brake activated, you hit the button to take off releasing the trans brake and into first you go.

You could launch at 5500 or 6000. (Everything is dependent on everything on where you launch from RPM wise.) Everything goes at once. "Launch" is the perfect word here. Like a rocket, everything engages at once and off you go. But your in your power band. Where you want to be.
And that is dependent on everything else. EVERYTHING