Indebted means owing money, or owing gratitude. Heavily indebted, indebted to her, deeply indebted.
The gratitude sense is the commoner in speech — I am indebted to you — and it is formal thanks with a suggestion that the debt cannot easily be repaid. The financial sense is technical: heavily indebted countries are a defined category in development finance. Note the silent b, added to show the Latin, as in debt.
1adjectiveindebtedOwing money.
“The family became heavily indebted after borrowing to pay for the new roof.”
2adjectivegratitudeOwing gratitude.
“I'm deeply indebted to my teacher, who believed in me when nobody else did.”
indebted is a state of owing.
Practised in A Song of Ice and Fire