Imagine counting paths from the top-left corner to the bottom-right corner of a grid. Can = "number of paths after steps" work? No. Knowing you took 5 steps tells you nothing about WHERE you are.
You could be at cell or . You need to track both your row and column: = "number of paths to reach cell ." Now the state captures everything you need: your exact position in the grid. When one number can't capture the full situation, you add another dimension. This is the core insight of multi-dimensional DP.