You are building a DoG pyramid. The output of each level of the pyramid is a DoG, which is composed of subtracting one Gaussian filtered image from another. Each of the two input Gaussian images are filtered with different Gaussian Filters, that is, with different sigmas.
The DoG output at each level should show stuff at the scale of that level. So at higher resolution, you will see edges and blobs at a fine scale. At the lower resolutions, you will see edges and blobs at a larger scale. What does this mean with respect to edges? Well, it means that edges that are many pixels wide at the high resolution will show up well at the lower resolution. It sometimes turns out that edges will show up at all the levels of the DoG pyramid.
To go to the next level of the pyramid, one first starts with the lesser filtered gaussian image at the current level, that is, the one with the smaller sigma. Subsample it down by 2 in each dimension. One can just subsample the pixels directly, as there is no need to filter (i.e. average the pixels in the local area) first, as this has already been done.
Then repeat the process at the current level.
As so on for the next levels.