Negative numbers
When you subtract the mean, all differences will be centered around zero. So if you present your data in a barplot, the bars may suddenly be negative. However, how you apply standardization can have quite a different effect.
Scale
When you divide by the standard deviation, the data will have variance and standard deviation equal to one. Hence the difference in scale.
My normalized data are normal (by definition...)
By what definition exactly? They just have mean $0$ and variance $1$. They don't look normal to me and there is no reason why standardization would yield normally distributed data.