Can you shed some light on this verse of the Quran (4:59) so I may understand and apply its meaning to my life.

This verse describes the position of authority to which we must be obedient. Thus, in applying this to our life we must first adhere to what they say with conviction and remain persistent. When trouble happens, we must turn and take recourse in their code of morality and justice. As such, the verse emphasizes our alignment with Ahl al-Bayt.