archivar

The everyday verb for filing or archiving — physical documents in a cabinet, or, just as commonly now, digital files, emails, and folders on a computer. Also used figuratively for shelving a plan or closing a case (archivar un caso).

• Archivé todos los correos del proyecto en una carpeta. — I archived all the project emails in a folder.
• El juez decidió archivar el caso por falta de pruebas. — The judge decided to shelve the case for lack of evidence.
• Hay que archivar estos documentos antes de fin de mes. — These documents need to be filed before the end of the month.

Using archivar to mean "to delete" — archiving keeps something in storage for later reference, it doesn't destroy it, so eliminar or borrar is what's needed for actually getting rid of something.