Definition of Dukkha

What is the precise meaning of the word "dukkha", often translated as "suffering" in Buddhism? Is it correct to say that Buddhism gives a method to get rid of **all** sufferings, including the most basic physical suffering (=illness/pain etc.)? So in that case even if some disease has no cure with our current medicine, Buddhism somehow has a way to free us from the pain of this disease? Please if possible provide a precise reference.