total+=!used[str[i]-'a'];
used[str[i]-'a']=1;
It is the condition for checking the characters and saving the value in the variable total.
The total variable will contain the number of unique characters in the array str.
This happens because you increment the count(total+=!used[str[i]-'a']) only if you haven't already marked the character as visited. If you incremented it, you mark it as such in the next line (used[str[i]-'a']=1) so that you wont count it again.
The notation str[i]-'a' is used to shift the ascii values of the characters from 0 to 25 (instead of 97 to 122) so that you can spare some space in the array.