It's not about resolution. Part of the reason those images look so pixelated is because they're quantized down to 2 bits per pixel: you only get white, light gray, dark gray, and black. Any intermediate shades have to be represented by dithering, which is what creates that stippled, checkered appearance.

If the images had the same resolution but higher bit depth, you wouldn't be able to make out much more detail, but the images would be a lot smoother and less blocky-looking.

EDIT: I used today's Wikipedia featured picture as an example.

Original: http://en.wikipedia.org/wiki/File:Kumar_Anish.jpg

256x256, 8 bits per pixel: http://i.imgur.com/YVIS2g3.png

256x256, 2 bits per pixel: http://i.imgur.com/iTFslZx.png

256x256, 2 bits per pixel, with dithering: http://i.imgur.com/LnlmORI.png