What do the colored squares on the bottom of packaging mean?

Those are the printer's color blocks.

When cereal boxes are printed, they use several different colors to create the image on the box. Every color that's printed has a "test" or proof square printed somewhere (that's usually not prominent) so the pressman can check that the ink has been transferred onto the "paper" with the correct density.

It's one of the ways printers ensure quality control on the printing. Manufacturers pay lots of money to design attractive packaging that will attract buyers. They want to be sure the colors and all the images are correct. This is one way the printer can be sure it's right.

You'll find these color blocks on nearly any printed packaging.