Here is a quick, class- and student-friendly explanation of three different models for multi-digit, whole number multiplication. As you can see, it shows the area model, the partial products method, and the "standard" or traditional algorithm.
It becomes obvious when we look at the three methods together that they simply organize the multiplications differently. Each method separates multiplication according to place value -- the value of the two digits being multiplied at any one time. The area and partial products methods make those separations explicit. They in turn help to clarify how the standard algorithm works.
I have become a big fan of the area model. I like to tell students that it's a "picture of numbers." Many must agree, because lots of our fifth graders continue to use it by choice long after they have mastered other methods.
I have an introduction to the area model for fourth and fifth graders in my TPT store, by the way.
Download the area model explanation (PDF).