Understanding non-linear dimensionality reduction algorithm (locally linear embedding)
To answer your first question:

Usually we want to reduce the dimension, because dealing with high-dimensional data is a pain: (a) algorithms for dealing with high-dimensional data tend to have higher computational complexity, and (b) high-dimensional data is hard to visualize and hard to understand.  If you can reduce the dimension without significant loss of effectiveness of the subsequent computational task, that can be useful.