(Normalize|Standardize) is a scale transformation on a numeric variable distribution to have:
- zero as mean (See Z score)
- the max and the min of the distribution into a given numeric range (normally between -1 and 1)
- zero mean and unit variance
The transformation to a Z scale is a standardization.
By normalizing, you get your data (variable) between 0 and 1 so the calculations aren't skewed by some attribute that happens to be on some gigantic scale
To Standardize a variables, you take the variable value and you divide it by the standard deviation of that variable over all the observations. See Statistics - Z Score (Zero Mean) or Standard Score
A standardize variable makes the variable and their coefficients comparable when they have different unit.