If you externalize something, you show or express it on the outside. You can externalize your anger at the poor quality of the food at the restaurant, but the other patrons would probably prefer you didn't rant at the waiter in front of them — so would the waiter.
Psychologically speaking, externalize is the opposite of internalize. You can externalize your fears in a constructive way by writing about them or drawing them, which will help you make sense of them. This is a much better solution than internalizing your fears, because you need to face them and deal with them once and for all. If you keep them bottled up, it is just like to cause you anxiety.