I still don't understand what that means?

Any test you would have to see "immunity" would show antibody levels. If these are raised, and show up, that means you were exposed to or had the disease in the past (or a vaccine). Zero Titres would mean you didn't have the disease yet. Titres (antibody levels) can be done for most diseases. They even do them on cats! In cats, repeated distemper vaccinations may lead to kidney failure from autoimmune reactions to the vaccine. In people, kids may be tested to see if they need booster to Tetanus, diptheria, or whooping cough. So those showing high titres in blood work, don't need the boosters yet.

For example, I show very high Zoster (shingle) titres and non-existant Simplex ones. My doctor says, most people test very high for Simplex even when showing no signs. Simplex is the Herpes virus that causes cold sores and genital herpes. My doctor said that my having very low titres to Simplex is very rare. Everyone tests positive just about for Simplex. I don't recall having a cold sore, but most kids are infected by age 3.
One would not recall an early event like that.

Chicken pox and Shingles are the same virus. Shingles is a recurrance in later life, when the immunity to the virus falls. Our immunity to Zoster, keeps it in check but when people get stressed, ill, or on chemo, that immunity can fall, and the virus reactivates.

So I would think if you had immunity that is measurable to Zoster virus, that means you had chicken pox in the past. Some people have mild cases, that are attributable to bug bites, etc.
"Natural immunity" in this country typically refers to having had the disease in the past (this typically is stronger and longer lasting). Artificial immunity is conferred by vaccines. This typically wears off and is weaker.

Sometimes doctors use "familiar" terms when telling patients things. And these terms may vary culturally and be confusing to say the least!