It is a personal alphanumeric code that uniquely identifies the subjects within the Italian State, as far as tax and administrative matters are concerned.
The tax code is one of the required documents to get the Residence Permit (Permesso di Soggiorno), to rent a room and open a bank account. Please note that the temporary tax code issued upon your registration on Alice web portal (the University of Pisa registration web portal) or Universitaly web portal is not considered as valid.
You can find all the info about how to book an appointment for the request of the Tax code here