What is a PayPal payer id?

It's just the id of the user who paid. You have to log it, to be able to give it to Paypal in case of conflict.

It's an external unique identifier of a particular PayPal account. Since email addresses change over time. A PayerID is static.

As others have said, payer_id can be used to identify a Paypal account. HOWEVER! -- a single Paypal account can have several payer_ids associated with it, one for each credit card or funding source used by that account. Because of this, a given Paypal account does NOT map one-to-one to a single payer_id.

For example, if Bob buys from my website (through Paypal) using his Visa card, the transaction will include one payer_id. If Bob later buys using his Mastercard, the transaction will include a different payer_id.

I confirmed this in a phone call with Paypal Merchant Technical Solutions, in May of 2013, after running into problems with my order processing (due to an incorrect assumption I had made about payer_id being a reliable way to see if a customer already existed within my customer database).

NB: One ramification of this fact is that, when writing a Paypal IPN-processing script, payer_id should properly be stored only in the "orders" database table, and not stored in the "customers" table.

See also this answer: Is the paypal payer_id unique per credit card?

EDIT: Apparently, each PayPal account does get just one payer_id. (That is not what I gleaned from my aforementioned phone call with Paypal Merchant Technical Solutions, but I can't find my notes on that call, so perhaps there was some confusion there.) Regardless, the payer_id does NOT uniquely identify a customer – as in a single, unique individual somewhere out there in the world. A customer could use multiple Paypal accounts, or could make some purchases as a "guest" using a different funding source than their primary Paypal account, and merchants would get different payer_ids for each one – even if the person's name, address, and all other identifying information were exact matches.

For these reasons, it is misleading for Paypal to call the payer_id variable a "Unique customer ID". Unfortunately, that description still persists in their documentation (scroll to the bottom of the "Buyer information variables" section):

https://developer.paypal.com/docs/classic/ipn/integration-guide/IPNandPDTVariables/#id091EB01I0Y4