What does "consumption-led growth" even mean?

Actually this post was just an excuse to post a picture of T-Pain.

There are a number of terms thrown around in the econosphere that confuse and annoy me. Perhaps they  annoy me because they confuse me? Anyway, one of these terms is "consumption-led growth" (and its evil sister terms, "investment-led growth" and "export-led growth"). This is usually invoked with respect to China. For example:

IMF officials “underscored the urgency of reforms to rebalance the economy toward more consumption-led growth,” the lender said. 

Or this:

Why hasn’t China done more to rebalance? The scale of the adjustment necessary to switch from an investment-led to consumption-led growth machine is so monstrous that the country would likely experience a lower rate of growth while it is taking place

Or this:

The transition from export- and investment-led growth to domestic consumption-led growth based on technology innovation, and from lifting tens of millions out of abject poverty to satisfying a more demanding middle class will be even harder for the party to execute.

What the heck is "consumption-led growth"? What does it even mean for a sector to "lead growth"?

Recall that GDP = consumption + investment + government spending + net exports.

Does "consumption-led growth" just mean that the consumption share of GDP should be higher than it is? If so, fine. Then why not just say "consumption-led GDP"?

Or does it mean that consumption should rise faster than the other components of GDP? Fine, but consumption's share of GDP can't increase forever. Eventually, consumption's share will hit a ceiling, and the "consumption-led growth" - if this is what it means - will be gone.

Or does it somehow mean that the shocks to GDP become shocks to consumption preferences, instead of shocks to productivity? That GDP grows because people want more stuff, not because people figure out how to produce more stuff? If so, it's a bit confusing as to how it would work. You can want more stuff til you're blue in the face, but only if you figure out how to make more stuff will you actually get what you want. Sure, you can work harder to get more stuff, but that kind of "growth" will pretty quickly hit a wall.

So what does "consumption-led growth" mean? I am a bit at a loss. Can someone explains what it means?