In the blue squares, the squares are enumerated in order, and we step through them to figure out which objects our ray is hitting first.
In 3D, 3D-DDA stands for 3D-Digital Differential Analyzer, which does the same process, but with 3d grid cells (voxels) instead of pixels.
Professor Pharr mentioned an algorithm for this process called "Bresenham's Algorithm," something I had not heard of. I thought it may be interesting to show the an introduction to the idea through a link I found (https://www.cs.helsinki.fi/group/goa/mallinnus/lines/bresenh.html), as well as its perks compared to a traditional 3D-DDA algorithm.
The primary benefit of the use of this algorithm is the reduction in use of floating point operations, which has the result of making it both more efficient and, interestingly, more accurate.