A Linear Regression Model with an interaction between two predictors (X1 and X2) has the form: 
Y = B0 + B1X1 + B2X2 + B3X1*X2.
It doesn’t really matter if X1 and X2 are categorical or continuous, but let’s assume they are continuous for simplicity.
One important concept is that B1 and B2 are not main effects, the way they would be if (more…)
I was recently asked about whether centering (subtracting the mean) a predictor variable in a regression model has the same effect as standardizing (converting it to a Z score). My response:
They are similar but not the same.
In centering, you are changing the values but not the scale. So a predictor that is centered at the mean has new values–the entire scale has shifted so that the mean now has a value of 0, but one unit is still one unit. The intercept will change, but the regression coefficient for that variable will not. Since the regression coefficient is interpreted as the effect on the mean of Y for each one unit difference in X, it doesn’t change when X is centered.
And incidentally, despite the name, you don’t have to center at the mean. It is often convenient, but there can be advantages of choosing a more meaningful value that is also toward the center of the scale.
But a Z-score also changes the scale. A one-unit difference now means a one-standard deviation difference. You will interpret the coefficient differently. This is usually done so you can compare coefficients for predictors that were measured on different scales. I can’t think of an advantage for doing this for an interaction.