The word quantum is derived from quantity, as it describes a fundamental indivisible unit of energy in modern physics theory.

In our everyday macroscopic world, we are used to energy being pretty much divisible as far as we care to play with it. As a concrete example, we can adjust the brightness of a light source continuously from painfully bright to so dim that it starts to be difficult, or even impossible, for us to see it. We don't see discrete steps at any point - the amount of light varies gradually and smoothly (assuming we have decent dimming circuitry).

Light behaves kind of like a fluid in this way, a stream of water if you will. We can vary a flow of water from a torrent to a trickle, setting it to any rate of flow we like in between. We aren't restricted to particular rates of water flow, because we can divide the water up as finely as we like and it's still basically water with the same properties.

Except that's not actually true when we get down to a submicroscopic level. Water is made of molecules (each one made of one oxygen atom and two hydrogen atoms, but that's an annotation in itself for another time). Each molecule is a discrete particle of water, which it is impossible to divide further (without becoming something other than water). So if we reduce the water flow enough, we eventually get to a point where we are letting a fairly small number of water molecules go by. We can imagine reducing the flow so much that we only let one molecule of water go per second. Or per minute, or even per hour.

There is still a flow of water, but it's no longer the smooth, rippling, infinitely divisible thing we are familiar with. It's like lumps of rock flowing past. Water is quantised - exists as discrete chunks of water - and the quantum of water is a water molecule. Water is grainy, but at a scale so small that we don't notice it.

It's the same thing with light. Light looks smooth and even and infinitely controllable to us. But it too is quantised, in tiny packets which we call photons. If you dim a light far enough (and not actually very far beyond the level where we can still see it), the light starts to look no longer like a continuous stream, but becomes detectable discrete chunks. Again, like the water, these chunks of light are so small that in our everyday life we never notice them. But they are there. Light is grainy, just like water.

And that's what a quantum is - the smallest possible unit of difference. So when advertising people say something is a quantum leap better than something else, they really mean it's so similar that you can't tell the difference.