According to the CN whitepaper key image I is generated thusly:
I = xHp(P)
I understand P is the one-time public key for the transaction, x the corresponding private key and H a deterministic hash function, but what is p?
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There are two hash functions you'll see referenced often with Monero - there is Hs and Hp.
Hs means "hash to scalar", meaning take a keccak(256) hash and then ensure the result is a "scalar" (a positive integer less than 2252 + 27742317777372353535851937790883648493).
Hp means "hash to point", meaning take a keccak(256) hash, interpret the resulting bytes as an elliptic curve point, and then multiply that curve point by 8 to force the resulting point to be in the base point group - i.e. to force it to be the case that there must exist an value x (even though x will be unknown) such that Hp(..data..) == xG.