In some countries the judge is chosen by the president, this opportunity for the president to having by his side judges that are nominated by him can bring judges aligned with the presidential philosophy that will then work towards his philosophy in their decisions.
Other way a presidential philosophy can impact judicial decision making is by embracing certain values and beliefs, this can give room for new interpretations of the law. Conservative, Liberalism or any political philosophy will suggest how the law must be interpreted, as it is strictly in the constitution or opening it up for new policies.