The padrón is a document signed at the town hall in which your address in Spain is registered. That is, it indicates exactly where you live, and with who.
Thus, it is a fundamental document to prove how long you have been living in Barcelona. If you want to apply for social arraigo, this is an essential proof.
This city registration is one of the first procedures you do once you arrive in Barcelona (or any other Spanish city). In fact, we advise you to do it in the first 2-3 days in the country to avoid any legal problem.
And not only will you need it, but the law requires you to register in the region where you reside regularly (more than 183 days a year, being a resident).
We are talking about a very quick procedure to do. In addition, it is completely free.
Keep in mind that you will have to do this process again in case you change your address.
