A generic cell, aka stem cell, during development gets signals which direct it to undergo certain changes and develop into a specific cell type. These signals can bind to certain DNA sequences which encode for certain genes required for the development of the stem cell into a particular cell type. After genes have been transcribed the cell undergoes many phenotypic changes. This whole process differentiates stem cells into certain cell types. The point of this is so that the organism can have its needs met for growth and development. For example, we need cells to develop our liver tissue. Stem cells get told (in a much more complex way than there would be time to describe here) to differentiate so that we can have an operational liver and in turn live.
This may not be the exact, generic textbook answer you are looking for, but the importance of cell differentiation is to be able to have certain tissues develop which are critical for function.