What is your definition of Quality?

The worst thing to do is to agree that each person could have a definition of a critical term like quality. Qality is defined at strategical level by following some of the schools or quality disciplines. But quality is a subjective term that has to be converted into objective ones after taking the strategic definition. So, if your question is because the subjective matter of quality then it could apply in this context.

Also for processes (quality assurance). If your process meets the requirements it will deliver a product that also meets the expectations.

Can it be aplied to relationships? I would tend to say that's more on the stakeholders knowledge area, but somehow it's all connected, isn't it?

As a newly PMP member, my definition is PMBOOK definition. Maybe in a future I'll have doubts about it.

Yes Sergio, I would add that Quality needed should be define according also the the purpose of the object (service or product).
The need of quality can be lower or higher according to the why we need the object. for example if it is for a temporary usage before final object is ready, quality will likely be lower.
Quality will be influence by many factor the corporate strategy is an important one, project/contract, stakeholders and usage will also influence.

Quality is the degree to which a product or service delivers its value to the intended user.

It is subjective and it may vary from what the manufacturer or service provider "thinks" the user will consider valuable in the product or service, and what the user actually values. And when I say the user, there are also user clusters with different quality expectations. So generalizing user we mean "the vast majority".

High and low quality, in this context, just mean above what the majority think is good quality or below that idea. It is specific for a market.

For example, a high quality car for the average underdeveloped country user may be considered a barely average car by an American user. And it's the same car.

To be free of defects is another definition, but a negative one. When one thinks of quality, one thinks of something "good", not simply "not bad".

Treat Quality as a plural and the answer becomes easy (at least for a product). What are the Qualities one expects out of the product? Each product will have a multitude of qualities and each individual will rank them differently, but the aggregation of the qualities forms the quality of the product.

I'm little unsure how to deal with the second question about relationships and processes. Yes, one can discuss the quality of a relationship or the quality of a process in the same manner as the quality of a product, but I am not certain if that is what is being asked.