Learn Spanish (Latin America): Necesitamos un aval a fin de que el banco otorgue la hipoteca. - We need a guarantor in order for the bank to grant the mortgage.

They mean the exact same thing ("so that" or "in order that"), but a fin de que is slightly more formal. You will often hear it in business, legal, or financial contexts like this one, dealing with banks and mortgages.

Why is the verb otorgar in the subjunctive (otorgue)?

Connectors of finality like a fin de que always require the subjunctive when there is a change of subject. The first part of the sentence is about what we need (necesitamos), but the second part is about what the bank does (el banco otorgue). Since the subject changes from "us" to "the bank", the subjunctive is triggered.

If the infinitive is otorgar, why is there a "u" in otorgue?

To keep the hard "g" sound! In Spanish, the letters "ge" make an "h" sound (like in gente). Whenever a verb ends in -gar (like jugar, pagar, or otorgar), you have to change the "g" to "gu" before an "e" in the subjunctive so that it doesn't change its pronunciation.

Can un aval refer to the person or the document?

It can be both! Depending on the context, un aval can mean a "guarantee" or "endorsement" (the agreement itself), but it is also commonly used to refer to the "guarantor" or "co-signer" (the person providing the guarantee), which is what it means in this sentence.