From Oxford Dictionaries:
Think about (something) carefully, especially before making a decision or reaching a conclusion
A common mistake is to use it interchangeably with think. Think is a more general word, used across a wide variety of situations where someone has a thought, idea or opinion. Ponder is far more specific and only used where someone is considering a choice or issue very seriously and with much effort.
In a narrative piece:
John used to think that Sarah wasn’t very interested in him.
Could she actually be interested in me? John pondered Sarah’s laughter to his joke that morning.
In a text essay:
As an immature young man, John made the mistake of dismissing Sarah because he thought she was not beautiful enough.
Sarah’s insightful remarks after the accident led John to ponder his past behaviour towards her, demonstrating his growing maturity.
I hope that was helpful!