on approval Definition

1. A favourable opinion; esteem.

Thesaurus: regard, esteem, favour, admiration, praise, respect, acclaim, liking, appreciation.
2. Official permission.

Thesaurus: sanction, endorsement, support, consent, permission, acquiescence, agreement, validation, OK, blessing, go-ahead, green light (slang).

Said of goods for sale: able to be returned if not satisfactory.