The padrón has nothing to do with your visa or your residence permit, and everything to do with the town you actually live in. Skip it and the health card, the school place and a few renewal appointments quietly become someone else's problem instead of a form you sign in twenty minutes.
The padrón is the list each ayuntamiento keeps of everyone who lives in the municipality. It is a local record of residence, not an immigration document. Your NIE is a tax identification number and your TIE is a residence card; the padrón is only about which town has to count you for schools, health centres and rubbish collection. You can be perfectly legal in Spain and still not appear on any padrón, and that gap causes more everyday friction than a missing permit.
For a tenant, the rental contract is normally the proof of address. Your name needs to be on it. If you are moving into a partner's flat, sharing with friends, or living in a house where the lease is in the owner's name, the ayuntamiento will ask for an authorisation signed by whoever holds the contract, plus a copy of that person's ID.
You book a cita previa through the ayuntamiento, go in person at the town where you really sleep most of the year, and hand over the documents. In Barcelona the wait for an appointment can run into weeks in busy periods. In the Maresme towns, Alella, Cabrils, Teià, Sant Andreu de Llavaneres and the rest, it is usually a matter of days, and some accept the paperwork online with a digital certificate.
You walk out with a volante or certificado de empadronamiento, which proves your address. Most banks and public offices accept one dated within the last three months. The registration itself does not expire for a Spanish or EU citizen, but non-EU residents without permanent residence have to renew it every two years. Miss that renewal and the town can strike you off the padrón, which tends to surface at the worst moment, usually during a residency renewal or a hospital visit.
Almost every other piece of family admin hangs off the padrón. The tarjeta sanitaria through CatSalut needs it, school enrolment prioritises the catchment area where you are registered, and the TIE renewal file looks a lot thinner without it. Some expat families wait until they are settled before dealing with it, then discover the appointment queue is the longest thing in their first month.
One practical note for anyone renting a villa in Maresme. Register at the address you actually occupy, not at a friend's flat in Barcelona because the queue is shorter there. A padrón that does not match where you live causes problems later with health coverage and school allocation, and in a small town the mismatch is noticed far more easily than in the city.