The key is 128 (binary) bits. That's all it means.
AES supports key sizes of 128, 192, or 256 bits.
AES has a fixed block size of 128 bits, which means it en/decrypts data in chunks of 16 bytes at a time. The plaintext/cipher text can be any length of course (and is padded out to a multiple of 16 bytes).
Good crypto implementations will use a Key Derivation Function which takes a password (or keyfile, etc) of any length, and generates a key suitable for the encryption algorithm in question.