python max function using ‘key’ and lambda expression

I come from OOP background and trying to learn python.
I am using the max function which uses a lambda expression to return the instance of type Player having maximum totalScore among the list players.

def winner():
    w = max(players, key=lambda p: p.totalScore)

The function correctly returns instance of type Player having maximum totalScore.
I am confused about the following three things:

1. How does the max function work? What are the arguments it is taking? I looked at the documentation but failed to understand.
2. What is use of the keyword key in max function? I know it is also used in context of sort function
3. Meaning of the lambda expression? How to read them? How do they work?

These are all very noobish conceptual questions but will help me understand the language. It would help if you could give examples to explain.
Thanks