Learning to learn.
That's a strong statement just to put learning to learn for the intuition of meta-learning. Of course it is not wrong to address it in that sense, but I believe it requires more explanation before sticking a label like that.
Let's first take peak at the main problem.
One of the issues with machine learning methods is that it usually requires large amount of data and extensive amount of computation power to be able to learn the simplest tasks. We would like to have a magical model that can learn with the minimum amount of data and we want it to be fast to get there.