NEON is an SIMD instruction set on ARM core CPUs. It helps to improve performance of an App. that does computationally complex jobs, such as image processing and 3D graphics.
I looked for tutorials for beginners, but there are not much. I found the following 4 posts. They explain basics of NEON step-by-step.
Coding for NEON - Part 1: Load and Stores
Coding for NEON - Part 2: Dealing With Leftovers
Coding for NEON - Part 3: Matrix Multiplication
Coding for NEON - Part 4: Shifting Left and Right