owe (someone) a favor

Translations
быть должным (кому-то) услугу
I owe him a favor for helping me move last weekend.
Я должен ему услугу за помощь в переезде на прошлых выходных.
Definitions
To be in a position of obligation to someone for a kind act or assistance they have provided, indicating that one should return the favor in the future.