meaning - How is "per se" used?

Here are some further definitions:

Chambers
per se adverb
in itself; intrinsically • not valuable per se.
ETYMOLOGY: 16c: Latin, meaning 'through itself'.

intrinsic adj
1. belonging to something or someone as an inherent and essential part of their nature. > 2. [not relevant]
intrinsically adverb.

Oxford Dictionaries (ODO)
adverb
by or in itself or themselves; intrinsically: it is not these facts per se that are important

Dictionary.com
per se adverb
by, of, for, or in itself; intrinsically: This candidate is not a pacifist per se, but he is in favor of peaceful solutions when practicable.
Synonyms: innately, inherently, indigenously, fundamentally.

Merriam-Webster
per se
adverb
by, of, or in itself or oneself or themselves : as such : intrinsically
adjective
being such inherently, clearly, or as a matter of law

intrinsic adj
1a. belonging to the essential nature or constitution of a thing
[other definitions not relevant]

Merriam-Webster Learner's Dictionary
per se adverb
by, of, or in itself — used to indicate that something is being considered by itself and not along with other things ▪ She feels that there is nothing wrong with gambling per se, but she thinks that it should be done in moderation.

One word that carries through most of those definitions is intrinsic, intrinsically, and I think that is probably the best synonym, but look also at the other synonyms listed. I think another particularly helpful definition of intrinsically is belonging to the essential nature or constitution of a thing.

Looking at some of the examples given above:

not valuable per se

An item may not be instrinsically valuable - it may not be worth a lot of money, or would not sell for much - but it may be valuable to the owner, perhaps because of memories associated with it, or because it has been passed down through the family, etc.

it is not these facts per se that are important

The facts on their own may not be important - but taken together with other information, they then become important.

This candidate is not a pacifist per se, but he is in favor of peaceful solutions when practicable.

He is not a pacifist just as a basic principle, or just because he has a fundamental belief that war is wrong - but he does believe that peaceful solutions should be used whenever possible.

She feels that there is nothing wrong with gambling per se, but she thinks that it should be done in moderation.

She thinks that there is nothing fundamentally wrong in principle with gambling - or, nothing intrinsically wrong with gambling - or, nothing wrong with gambling in itself - and the implication is that it's all the other things associated with gambling (e.g. getting addicted to it; spending lots of money) that are wrong.