Immunity is the ability to resist disease. This can mean fighting off bacteria and viruses before they cause disease, or, in certain situations, that a pathogen cannot infect an individual because it can't infect cells. An example of the first situation is immunity by prior exposure; you get vaccinated against an antigen, and your body can recognise it and mount a strong response quickly, clearing the antigen before it can cause disease. An example of the second: there's a genetic variant that causes a change in protein structure, that means the HIV virus cannot bind and enter the cells of individuals with this variant.
Tolerance is more like ignorance; the potential antigen is there, but the immune system doesn't react to it. This can be beneficial - our immune system doesn't (usually) recognise proteins present in our own bodies. The word tolerance is usually used when the body is capable of mounting a response, but doesn't. HIV can avoid detection. The immune system isn't 'tolerating' HIV.