What does it mean to say that multiplication is distributive?

The property which states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.

In other words...
If we are multiplying a number by two other numbers that are added together inside parentheses, it is the same thing as multiplying the number on the outside of the parentheses by each number inside and  then adding those two results.

3 * (1 + 2)	=	(3 * 1) + (3 * 2)
3 * 3	=	3 + 6
9	=	9

(4 + 7) * 5	=	(5 * 4) + (5 * 7)
11 * 5	=	20 + 35
55	=	55

The distributive property is also a way of re-grouping numbers.

Let's take a look at a simple example,  2 x ( 3 + 2) = (2 x 3) + (2 x 2)

+	=	+

The left-hand side of the equation is represented by two groups of three and two fingers each. The right-hand side of the equation is showing us two groups of three fingers and two groups of two fingers.
Count the fingers on both sides of the equation. They both total 10 fingers.