This is an excerpt from Computer Network by Andrew S. Tanenbaum page 206.
A code is a collection of binary vectors of some length $n$, known as codewords. The Hamming distance between two codewords $x,y$ is the number of positions $i$ such that $x_i \neq y_i$. The minimum distance of a code is the minimum Hamming distance between two different codewords.
For example, the Hamming(7,4) code consists of 16 codewords of length 7:
0000000 1110000 1001100 0111100 0101010 1011010 1100110 0010110 1101001 0011001 0100101 1010101 1000011 0110011 0001111 1111111
You can check that any two codewords differ in either 3 or 4 positions. For example, 1010101 and 0100101 differ in the first 3 positions. Therefore the minimum distance of the code is 3.
There is absolutely no meaning for the Hamming distance of a single codeword. Hamming distance is a property of pairs of codewords.
Tanenbaum is not saying that ASCII character "A" has a particular Hamming distance. Computerphile has a video that may clear things up.
The Hamming distance between two codes is the number of times there is a different bit between them, for example between
1111 a Hamming distance of 1.
The example that you're seeing is code correction. When you send anything through a cable there could be some errors (change of bits
1 to 0 or
0 to 1). So there are some common algorithms that minimise these errors within the domain of Information Theory. In this example they show the binary code of the letter A before and after being received by destination, a Hamming distance of 3 was found means that 3 bits have changed.
I previously implemented some related functions and more details are explained on my GitHub. You can check my git repository if you're interested.