«A penny for your thoughts» is a saying to ask other person what he or she is thinking.
It means you pretend to give someone a penny (penique / centavo) if he or she says what bothers him/her as a way to express interest in his/ her life and problems.
And you can watch this video regarding its pronounciation:
The other expressions she teaches are:
– A penny saved is a penny earned
– Penny wise and pound foolish
Caedmon's School of English 