When we use the phrase 'private parts' do we refer to 'thighs' also or this phrase only refers to parts like urinary organ, hips, etc?
Private parts is an euphemism for genitals.
(plural noun) euphemistic:
A person's genitals.
the sexual organs; the testicles and penis of a male or the labia, clitoris, and vagina of a female.
Private parts may also include the anus, perineum, pubic-area, nipples and possibly breasts - depending on the person speaking.
The phrase is also sometimes shortened to just privates.
This means that the thighs and hips are not commonly included in the meaning of the phrase.
If referring to wanting to keep these other areas covered, a general phrase in common use is:
Not wanting to show too much skin
Which implies wearing clothing that covers areas such as the hips, thighs, legs, shoulders and chest (depending on which areas the person considered private to them).
In the English-language children's book "Your Body Belongs To You", the term "private parts" is described as being "all those parts covered by your bathing suit".
This is a simple, broad definition to which we all can relate. It also respects the culture in which someone lives. Which I think matters, particularly for women. Compare for example bathing in Cleopatra's Bath in Egypt, vs the sunny shores of Perth, Australia.
So, to your question,
does it include thighs and hips
I'd say: it depends. Gender, culture, and personal preference define what's private and what's not, and you need to consider the nuances when using this term.
The expression private parts only refers to a person's genitalia. That would typically be the penis in the case of a male and the vulva in the case of a female. This means that other body parts such as thighs, hips etc. are not considered private parts. They are body parts, but not private. Private parts are supposed to be completely private. That is, no one should see them when you're in public. For example, when you're at the beach, are the people there generally able to see your thighs and hips? I would think so. But they're not able to see your private parts because they're hidden under the swimming trunks that you're wearing.