When training a model (whether it is Neural Network based or not) the most important part is the amount and quality of the data used to train it.
The more good data you have, the better you will be able to train your model.
However, the more data you have the more time it takes to train your model. So if you can reduce the dimensions you can optimize training.
Other advantages of Dimensionality Reduction include:
- Easier to interpret
- Avoids the The insight behind the term coined by Richard E. Bellman is ... More
- Reduction of variance
There are two ways of reducing the number of dimensions: extraction & selection, see Feature Selection versus Feature Extraction.
Some examples of techniques of Dimensionality Reduction are: A kind of Dimensionality Reduction. and LCA.