Understanding how to create atoi; How are characters compared?

Question

I am trying to improve my understanding of C++, pointer arithmetic especially. I use atoi pretty often, but I have rarely given thought as to how it works. Looking up how it is done, I understand it mostly, but there is one thing that I am confused about.

Here is an example of a solution I have found online:

int atoi( char* pStr ) 
{
  int iRetVal = 0; 

  if ( pStr )
  {
    while ( *pStr && *pStr <= '9' && *pStr >= '0' ) 
    {
      iRetVal = (iRetVal * 10) + (*pStr - '0');
      pStr++;
    }
  } 
  return iRetVal; 
} 

I think the main reason I have had a hard time grasping how atoi as been done in the past is the way characters are compared. The "while" statement is saying while the character exists, and the character is less-than-or-equal-to 9, and it is greater-than-or-equal-to 0 then do stuff. This statement says two things to me:

1. Characters can be compared to other characters logically (but what is the returned value?).

Before I looked into this I suppose I knew it subconsciously but I never actually thought about it, but a '5' character is "smaller" than a '6' character in the same way that 5 is less than 6, so you can compare the characters as integers, essentially (for this intent).

1. Somehow while (*sPtr) and *SPtr != 0 are different. This seems obvious to me, but I find that I cannot put it into words, which means I know this is true but I do not understand why.

Edit: I have no idea what the *pStr - '0' part would do.

Any help making sense of these observations would be very... helpful! Thanks!