Let us step away from definitions for a moment and try and understand what we mean when we say - "This apple is of the highest quality". A lot of answers I have got just say - it means it is the best - but my question is best against what ? So there is a comparison - there is a comparison against a perception or an expectation. Everyone has expectations when they go to buy a service or product and when those expectations are met the person is satisfied with the product or service and that is when the product or service is deemed to be of quality.
Different people have different expectations of the same product. So each one of their perceptions of what is a quality product or service may be different. For example someone may want cheap apples that are not spoilt to make jam, another may want a sweet, crunchy, red apple to gift someone irrespective of the cost. So each one of their perceptions of quality is different. Hence it is important to understand the expectations of the person in order to provide them quality services and products.
In software the expectations of the customers need to be captured during the requirements definition phase. The better the expectations of the customer are captured the higher are the chances of satisfying the customer with a quality product.