The BIN + Aeroplan Number + Code creates a standard 16-digit card number.

627421 is the Issuer Identification Number (aka Banking ID Number or BIN) for Aeroplan.

The next nine digits are your card number.

The "code" is a checksum calculated using the industry-standard Luhn Algorithm.

Put them together and you have a standard PAN (Personal Account Number) ready for processing by point of sale devices and other payments equipment.