I am new to cryptography. I am looking to understand how to answer this question from my class:
Find below the S-box of AES. Given the input 01010011 in binary, calculate the output.
An AES S-box is nothing else than a permutation. You give it a input, and it give you the corresponding output.
Here the S-box is represented by a 2D array. If your input is $01010011$, you have to get it's hexadecimal representation : $0x53$ (because an hexadecimal is represented by four bits, $0101 = 5$ and $0011 = 3$).
Now you only have to get the corresponding output of the Sbox ($5$ is the left nibble, en $3$ the right nibble).