but I could never quite figure out what I was supposed to do with them. I mean, do they make a picture? Do they make a solid rectangle?!

They make a solid rectangle. Several of them, if I recall correctly.

I think it only took four pieces to make a single punchcard. But you had to flip the pieces around and change their colors to make them fit. Clever!

The trick was realizing that each piece was the result of two "cuts" by a cookie-cutter style punch. You eventually came to learn what each of the cookie-cutter shapes were. One was concentric arcs, one was a tab-and-groove shape, etc. There were several of them.

The interesting thing was that the various cuts resulted in both parts of the shape, i.e., a positive image and a negative image of the cookie cutter. So a negative tab-and-groove combined with the positive concentric arc shapes would produce a completely different image than the reverse versions.