What is a definition of the idealized style?
Idealized style in art is just that -- making art that depicts a human ideal. This type of art aims for perfection. If we are referring to an idealized painting of a woman, for example, the woman will have a perfect, ideal shape. She will be beautiful with beautiful features, a desirable appearance, etc. This type of art emphasizes perfect characteristics and features.
Naturalism or realism, on the other hand, aims to portray art exactly as it is. Art that subscribes to naturalism or realism doesn't shy away from showing imperfections. In this type of art, you may see a woman in her natural state, perhaps a little fat, perhaps with a crooked nose if that's what she has. There is no attempt to beautify or perfect appearance. It is presented in its natural form.
Before the 19th century, idealized art was the norm. After the 19th century, naturalism and realism movements in art became more dominant.
An example of realist work is Rembrandt's painting "Hendrickje."
Raphael's paintings are examples of idealized art.
The concept of anything being idealized is simple: there are no blemishes or flaws or faults in something which is idealized. Somehow, it is above the ordinary. That can certainly be taken literally, as in a painting of an apple with no flaws or bruises of any kind and a color that is beyond real, but it's really more than that.
Think about it this way--when someone is in love, especially the first flush of love, it's difficult to see anything but the positives about the loved one. What's more, even those wonderful qualities are seen as near perfection. Others see the flaws, but the loved one does not. In art, that can mean deifying a subject--making a god (or goddess) out of a mere mortal. It could be creating an item which is beyond realistic; that's what moves it to the ideal. For example, almost all paintings of Mary, mother of Jesus, are idealized. I'm confident you can think of some more examples on your own of artwork in this idealized style.