lambda is an anonymous function, it is equivalent to:

def func(p):
   return p.totalScore     

Now max becomes:

max(players, key=func)

But as def statements are compound statements they can't be used where an expression is required, that's why sometimes lambda's are used.

Note that lambda is equivalent to what you'd put in a return statement of a def. Thus, you can't use statements inside a lambda, only expressions are allowed.

What does max do?

max(a, b, c, ...[, key=func]) -> value

With a single iterable argument, return its largest item. With two or more arguments, return the largest argument.

So, it simply returns the object that is the largest.

How does key work?

By default in Python 2 key compares items based on a set of rules based on the type of the objects (for example a string is always greater than an integer).

To modify the object before comparison, or to compare based on a particular attribute/index, you've to use the key argument.

Example 1:

A simple example, suppose you have a list of numbers in string form, but you want to compare those items by their integer value.

>>> lis = ['1', '100', '111', '2']

Here max compares the items using their original values (strings are compared lexicographically so you'd get '2' as output) :

>>> max(lis)
'2'

To compare the items by their integer value use key with a simple lambda:

>>> max(lis, key=lambda x:int(x))  # compare `int` version of each item
'111'

Example 2: Applying max to a list of tuples.

>>> lis = [(1,'a'), (3,'c'), (4,'e'), (-1,'z')]

By default max will compare the items by the first index. If the first index is the same then it'll compare the second index. As in my example, all items have a unique first index, so you'd get this as the answer:

>>> max(lis)
(4, 'e')

But, what if you wanted to compare each item by the value at index 1? Simple: use lambda:

>>> max(lis, key = lambda x: x[1])
(-1, 'z')

Comparing items in an iterable that contains objects of different type:

List with mixed items:

lis = ['1','100','111','2', 2, 2.57]

In Python 2 it is possible to compare items of two different types:

>>> max(lis)  # works in Python 2
'2'
>>> max(lis, key=lambda x: int(x))  # compare integer version of each item
'111'

But in Python 3 you can't do that any more:

>>> lis = ['1', '100', '111', '2', 2, 2.57]
>>> max(lis)
Traceback (most recent call last):
  File "<ipython-input-2-0ce0a02693e4>", line 1, in <module>
    max(lis)
TypeError: unorderable types: int() > str()

But this works, as we are comparing integer version of each object:

>>> max(lis, key=lambda x: int(x))  # or simply `max(lis, key=int)`
'111'

max(a,...) is always going to return an element of a. So the result will be either 1,2,3, or 4. For each value w in a, the key value is b[w]. The largest key value is 10, and that corresponds with w equalling 1. So max(a,key=lambda w: b[w]) returns 1.

From https://www.programiz.com/python-programming/methods/built-in/min:

1. min(iterable, *iterables[, key, default])
   • iterable - sequence (tuple, string), collection (set, dictionary) or an iterator object whose smallest element is to be found
   • *iterables (Optional) - any number of iterables whose smallest is to be found
   • key (Optional) - key function where the iterables are passed and comparison is performed based on its return value
   • default (Optional) - default value if the given iterable is empty

The call min(stocks, key= lambda x:stocks[x]) is finding the smallest element in stocks, by comparing the results of the function lambda x:stocks[x], which is just an anonymous function that returns the value of the stock for a given key. So the call to min returns the stock with the smallest value.

See also Get the key corresponding to the minimum value within a dictionary and http://www.aroseartist.com/python-dictionary-max-min/