The term "Grid" here is used somewhat loosely. The first number is the number of categories, and the second number is the number of items in each category.
So you are going to end up with some arrangement of squares and each square is defined by the second number. (e.g. in a ?x3 grid you will end up with several 3x3 boxes connected together)
The number of boxes is a bit trickier to describe. I hope someone else can come in and give a simpler version than what I'm about to write. You have exactly one box to compare each of the categories with. Let's think about writing the grid from left to right. So we define one category as our first column and then fill in the rest as our rows. Since we don't compare a category to itself we end up with the long side being one less than the number of categories. Then we take the last category in the rows and make it the next column. But we drop of the bottom box where it would be compared to itself. On and on until we end up with only one row being used. If my math is right, the total number of boxes you end up with is (c*(c-1))/2 where c is the number of categories.
Solving them takes some practice, don't be afraid to use this game's help button. It will give you the next logical move and tell you how you should know it. Ultimately it comes down to knowing that none of the people/objects have anything in common in the categories. So if I know James is wearing a blue shirt I know that no one else is wearing a blue shirt. And since the two are linked, anything I know about the person wearing blue I then know applies to James (and vice versa).