Could someone please explain what this slide and the next one actually portray?
These slides show a common artifact that arises in texture filtering: aliasing due to "minification." The scenario is that the region covered by a single pixel in image space corresponds to a very large region (many pixels) in texture space. Therefore, if you use only a single sample per pixel, you will sample a random (or more properly, arbitrary) 'texel' from the texture. Visually, the result is jaggy edges, and ugly "crawling" artifacts when the scene is in motion. One solution is to use supersampling, which may help a little bit but will never do a very good job of solving the problem: for instance, even with 16x16 supersampling, a single pixel may still cover 100x100 or 200x200 texels---consider for instance what happens as the camera zooms away from an object. So, a better solution is to use prefiltering, i.e., instead of trying to do the filtering at render time (using supersampling) you store a filtered version of the texture ahead of time. This not only saves a ton of work, it also allows you to effectively use arbitrarily large filters: 1x1, 2x2, 4x4, 8x8, 16x16, ... by just recursively downsampling the base texture by a factor of 2. This technique is what is known as "MIP mapping," and is explained later on the slides. No way to reach this level of performance using supersampling; it's just the wrong solution here.