What are the advantages using Principal Components as input for neural networks compared to using "normal input" for neural networks?
You can read a nice description of PCA here.
The advantage of PCA (one method of dimension reduction) in the context of ML (ie. neural networks) would be to reduce the risk of over fitting and reduce computational complexity.
You could also phrase your question as: what are the alternatives to PCA? For PCA vs Partial Least Squares, see this Cross Validated post For PCA vs random subspace projection see this Cross Validated post
I think this question has been asked countless number of times here... You want PCA because you want to reduce your input size and thus improve training time and less likely to overfit.