Your residence permit in Spain is a card that has your NIE number on it.
There are two types of cards:
Applying for your TIE residence permit
Getting your residence permit is the final step in immigrating to Spain. You apply for your residence permit in the province where you are planning to live. You apply at an Oficina de Extranjeros or, if that doesn't exist in your province, in the Comisaría de Policía.
If there is an address change, or your nationality or family situation changes, you must notify this same office of the change within one month.
The TIE is proof of your identity, and of your right to stay in Spain longer than 6 months.
Getting a residence permit for British citizens
How does the visa process work?