Why isn't it said, (Yo hambre) ? In stead of, (Tengo hambre).
The full sentence is "Yo tengo hambre" but you don't need the yo as it's already known when you use the word "tengo."
"hambre" is a noun > "hunger". Literally Spanish says "I have hunger", a concept used in German, Dutch, French and Italian also. As "I have hunger" is bad English you must translate "I am hungry"