Why do stores require signatures on credit card receipts and swipe machines?

Audit purpose.

Used to be that merchants were required two things of a credit card transaction:

1. The actual swipe of the physical card and
2. the autograph to match it to the card owner (and/or to verify it against other forms of signature based identification).

This would then serve as proof of sale as far as the merchant was concerned, should the card owner ever try to reverse the transactions (in the event the card is lost, the signature replica would have some noticeable differences to the discerning eye).

Nowadays, some merchants don't require signature below a certain value (on which I cannot comment why).