To understand what is going on, let's take one letter(repeated more than once) in the sentence string and follow what happens when it goes through the loop.
Remember that we start off with an empty characters dictionary
characters = {}
I will pick the letter 'e'. Let's pass the character 'e' (found in the word The) for the first time through the loop. I will assume it's the first character to go through the loop and I'll substitute the variables with their values:
for 'e' in "The quick brown fox jumped over the lazy dog.":
{}['e'] = {}.get('e', 0) + 1
characters.get('e', 0) tells python to look for the key 'e' in the dictionary. If it's not found it returns 0. Since this is the first time 'e' is passed through the loop, the character 'e' is not found in the dictionary yet, so the get method returns 0. This 0 value is then added to the 1 (present in the characters[character] = characters.get(character,0) + 1 equation). After completion of the first loop using the 'e' character, we now have an entry in the dictionary like this: {'e': 1}
The dictionary is now:
characters = {'e': 1}
Now, let's pass the second 'e' (found in the word jumped) through the same loop. I'll assume it's the second character to go through the loop and I'll update the variables with their new values:
for 'e' in "The quick brown fox jumped over the lazy dog.":
{'e': 1}['e'] = {'e': 1}.get('e', 0) + 1
Here the get method finds a key entry for 'e' and finds its value which is 1. We add this to the other 1 in characters.get(character, 0) + 1 and get 2 as result.
When we apply this in the characters[character] = characters.get(character, 0) + 1 equation:
characters['e'] = 2
It should be clear that the last equation assigns a new value 2 to the already present 'e' key. Therefore the dictionary is now:
characters = {'e': 2}