Rough context: When the GPU (or the CPU back in the days) had to draw a texture, it had to sample pixels, maybe one, maybe four and do some say bi-linear filtering in between them, and then use that pixel as a result.
Now several problems:
1. If your texture is sampled roughly one pixel from it to one pixel on the screen, and if all pixels are read linearly ("horizontally"), then you are good with the cache, cause for the first pixel you've read the cache maybe cold at that address, but it'll load the next pixels just in case you need them, and here is the catch - you need to get always benefit from that - it's like always using your coupons, and deals, and your employer perks. So the CPU/GPU might read 4, 8, 16 who really knows (but you) bytes in advance, or around that pixel.
2. But then you turn the texture 90 degrees, and suddenly it's much slower. You draw a pixel from the texture, but then the next pixel is 256, 512, or more away ("vertically), and then next too, your cache line of 4, 8, 16, 32 or 64 read bytes that you did not used, and by the time you might need them again, the cache discarded them. Hence the slowness now - much much slower!
4. To fix it, you come up with "swizzling" - e.g. instead of the texture being purely scan-line by scan-line, you kind of split your image in blocks - maybe 8x8 tiles, or 32x32, and then make sure those tiles are linearly written one to each other. You can go even further, but the idea is that under any angle, if you decide to read, you most likely would hit pixels from the same cache line you've read before. It's not that simple, and my explantation is poor, but here is someone who can do that better than me: https://fgiesen.wordpress.com/2011/01/17/texture-tiling-and-...
8. But even with swizzling, tiling, whatever you call that magic to keep pixels together in any direction really together stops working as soon as you have to draw that big texture/image on a much smaller scale.
16. Say 256x256 would have to be drawn as 16x16 - And you say I don't need mipmapping, I don't need smaller versions of my image, I can just use my own image - well then nomatter how you swizzle/tile, you'll be skipping a lot of pixels - hop from here to there, and lost cache lines.
32. For that reasons mipmaps are here to help, but stay with me for one more minute - and see how they almost fix the shimmering problem of textures with "fences", "grills on a car", a pet's cage, or something like it.
64. And when you hear the artist ready to put real spider-man logo on the character made out of real polygons, and real grill in front of the car, made out of real polygons, and real barbed-wired made out of polygons very nice looking fence - then stay away, as these polys woulds shimmer, no good level of detail can be done for them (it'll pop) and such things are just much easily done with textures and mipmaps - it kind of solves a lot of problems.
