The rules entry on Heal is indeed not very comprehensive.
I'd think that healing should word the same way as taking damage/horror:
“Take X damage” is shorthand for “deal X damage to your investigator.”
“Take X horror” is shorthand for “deal X horror to your investigator.”
So "Heal X damage" is shorthand for "heal X damage from your investigator".
This is not actually in the rulebook. I asked Matt Newman (the designer), and he confirmed that it works the same way. He'll add it to the FAQ.
He said that you cannot heal your assets unless an effect specifically instructs you to do so. Reassigning damage/horror to assets is a special rule that only applies to taking damage.