To not be up to something simply means you don't have the energy of motivation to do it. For example, if you're feeling sick and someone asks you to go for a jog, you could say "I really don't feel up to that right now." Please feel free to contact me if you have any other questions.

To "not be up to <something>" in this case means you cannot rise to the occasion, your situation does not allow for it, or you are simply unwilling to do it. So it means you are unable or unwilling to do something. You may also hear "Not up for (doing something)" which expresses unwillingness rather than inability. ("I'm not up for going out tonight, I prefer to stay home". There is another meaning. "To be up to" can also mean what someone is currently doing. In informal, conversational English, you might hear this question: "What are you up to?" ... it means "What are you doing (now)?"