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> they were in some old Japanese character set

This implies that they're obsolete, but they're not -- they're still in very common use today. You can type them in Japanese by typing まる (maru, circle) and the number, then pick it out of the IME menu. Some IMEs will bring them up if you just type the number and go to the menu, too. :)

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Fair enough. I was thinking of them as obsolete, but shouldn't since you do see them a surprising amount in Japan.

What do the Japanese use the circled numbers for?

Ordinals and references, like this:

① Draw some circles

② Draw the rest of the owl

Commentary: ① is simple but ② is masking many complex steps that are necessary to draw an owl.

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