ord map from a local field to $\mathbb{Z}$

Question

I'm reading J. Milne's notes on class field theory and near in the section of the chapter on local CFT he speaks of an exact sequence $$1 \to U_L \to L^{\times} \xrightarrow{\textrm{ord}_L} \mathbb{Z} \to 1.$$ Here $L$ is a local field and $U_L$ is the unit group of the ring of integers of $L$. Maybe I missed something but as far as I can tell there is no explanation of what the map $\textrm{ord}_L$ is. Can someone fill me in? Thanks.