A power of attorney names someone — almost always a parent — who can sign on the missionary's behalf while they are away. It does not take anything away from the missionary, and it ends when they revoke it or when the term you choose runs out.
With one in place, a parent can file a tax return, deal with the bank, renew or cancel a phone plan or insurance policy, sign for a car sale or registration, respond to a student loan servicer, and handle whatever paperwork arrives in the mail with a deadline on it.
Without one, institutions will not talk to you. Banks and the IRS in particular will not accept a parent's authority over an adult child's account on the strength of the relationship alone, no matter how obvious the situation is.