Is AES key length a size of the key or entropy? While educating my self I'm having hard time to understand what an 128 bit AES key actually means?
Is it a key length or entropy?
Please explain to me trough following example (assuming AES):

Password length in characters (L) = 20 (characters)
Symbols used (N) = 95 (ASCII set)
Entropy = log2 (N^L) = 128 (is this what is called 128bit AES key?)
OR
Key length = L * 8bits = 160 bit key length ? (is this supposed to
be 160bit AES key?)

When somebody says that he's using 128bit AES key, I want to know to what is he referring to, a key length or entropy?
When they say they are using a 128 bit AES key, they mean the length of the key is 128 bits. Technically a 128 bit AES key could have 0 bits of entropy, 128 bits of entropy, or anywhere in between.

To be secure, however, the 128 bit key should also have high entropy. Ideally, a 128 bit AES key would also have 128 bits of entropy.

A few side notes
Keep in mind that $\log_2N^L$ only computes the entropy in the key if the $L$ characters in the password were chosen randomly.

There is no such thing as a 160 bit AES key. AES supports key lengths of 128, 192, 256 bits.