Chip: "something you have" factor. The card has a tamper-resistant chip, that holds cryptographic keys and does the signing.
Pin: "something you know" factor. Card owner enters a PIN code on the POS terminal's keypad. The card only allows the transaction after the correct PIN entry, and blocks in case of multiple errors.
No signatures required in this scheme. Except for the cryptographic ones, of course.
It works like this: you insert the card, type in[1] your PIN code that is supposed to be secret and then the purchase is authorized.
Requirement to enter the PIN lessens the fraud possibility in case of lost or stolen cards, and requirement to have the chip combats skimmers (if terminal is capable and card has a chip, swiping the magstripe instead of using the chip should result in rejection).
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[1] If prompted. Depending on the bank, infrequent low-cost low-risk purchases may not require a PIN code. Card keeps a list of recent purchases in the EEPROM and is probably capable of starting to ask the PIN code after number of purchases is over some threshold (but I'm not exactly sure how they're programmed).