The easiest way to understand natural rights is that they are a collection of activities (live, be free from coercion, pursue property) which, if respected, lead to a better outcome in society. The name "natural" does not indicate that they come about "naturally." Quite the opposite, actually, it is somewhat nonintuitive that living in a society with these rights will be better. That might be one reason they are so little respected.
In addition, the fact that they are rarely respected is, I think, a consequence of the historical circumstance that human society was constructed on the basis of slavery. It takes a lot of work to produce sustenance from natural resources, and it has been historically profitable for some to enslave others to do that work. Slavery is also the foundation upon which most human society is currently built.
It will take a paradigm shift and a lot of education to see natural rights respected, but we're making progress. The "natural" part does imply, I think, that making progress and moving in that direction is unavoidable.
Think of it like this: For a long time, people thought that a king was needed to own everybody and tell them what place to have and what jobs to do in society. It took a long time to figure out that monarchy was a rediculous system. A lot of people in the world still don't have it figured out, but there are a lot of people who have figured out they can live just fine without a king. Thus, it is unavoidable. A natural law: It's better not to have a king. You'll get a better society if you don't allow such idiocy.
Natural rights: It's better to not coerce people and let them act as if they own themselves. You'll get a better society if you don't allow the idiocy of people thinking they can run other peoples' lives.
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