The Chancellor is the head of the executive and the government. The President is the Head of State, but unlike other heads of State, he is not part of any of the classical powers. instead, he forms a fourth, neutral power. The President does not possess power but a lot of administrative importance, and his main purpose aside from representation is the supervision of legislature and executive, so no one can act against the law or the constitution. While he lacks respect by the people, he enjoys a lot of respect by other politicians, and even though he has no actual say on politics, his opinion is valued by them.
The position of the president is defined in the articles 54 - 61 of the German Basic Law, the political reality of the President can be seen when researching former presidents, such as Theodor Heuss (first President), or Horst Köhler (ninth president, one of the best-liked amongst the population).