Manifold learning is an approach in machine learning that assumes that data lies on a manifold of a much lower dimension. These manifolds can be linear or non-linear. Thus, the area tries to project the data from high-dimension space to a low dimension. For example, principle component analysis (PCA) is an example of linear manifold learning whereas an autoencoder is a non-linear dimensionality reduction (NDR) with the ability to learn non-linear manifolds in low dimensions. A comparison of linear and non-linear manifold learning is shown in the following figure:

As you can see from graph a), the data is residing at a linear manifold, whereas in graph graph b), the data is residing on a second-order non-linear manifold.