What does nonalkaline mean in shampoo?

It's talking about the pH of the shampoo itself. You shampoo's pH should be around 5-7, which is the pH of your skin (which is the middle of the pH scale). Acidic and Alkaline are the opposite ends of the pH scale, when it says Non alkaline shampoo, it means it's not high on the pH scale so it won't damage the cuticle at all. See relaxers are real high in Alkalinity