What makes a person's immune system stronger than another? Many factors. Genes play a fundamental role, to an extent. The genetic makeup a person has may lead them to require certain nutrients or higher/lower levels of nutrients, both of which may be implicated in their propensity towards a disease. The rest is up to your environment, behaviour, lifestyle, etc.

If you are born with a genetic predisposition, that gene may not be expressed until it encounters an environmental factor that signals it (including social and familial influences, and lifestyle choices). So if the environment signals the gene - that is epigenetics.

However, this also includes the mental environment. Mental and emotional stress is one of the greatest taxes on the immune system. Sympathetic nervous system overdrive causes adrenal fatigue, which takes energy from other bodily functions (such as the immune system, digestive system, etc.) to produce cortisol. In this case, our constant experience becomes our habitual environment, which stimulates an emotion (anger, frustration, depression, etc.). Therefore, if the environment signals the gene, then to an extent a gene's expression can be influenced by the mind/emotions.

In conclusion, many things make up the strength of someone's innate immune system. Nutrition, activity, neurochemical balance, gut flora (which affects mental health), toxic habits, thought patterns, genetics, environment etc. all play an essential role. Generally, in most 'standard' individuals in first world countries, low immune system function is caused by poor health choices and mineral/vitamin deficiency. That in turn affects mental health, creating chemical imbalances in the brain, as the brain needs sufficient micronutrients to function optimally (therefore, for the other bodily systems to function optimally).