Advanced Encryption Standard Algorithm Secret Key
One very important thing you are missing is the idea behind AddRoundKey and the Key Schedule.

Each round, there is a new round-key. The round key is derived from the main key. So, say you have a 128-bit block (AES) and a 256-bit key. The internal state is 128-bits and the round key is 128-bits. The specification states that for this configuration, there will be 14 rounds. Since the round-key changes for each round, it is easy to see that all 256-bits of the main key will be used over the 14 rounds.

To see exactly how all 256-bits of the main key are used, you'll have to dive into the details of the key schedule.