Amiable means good-natured and likable. It describes people. Amicable means characterized by goodwill. It describes relationships or interactions between people. So, for instance, two amiable people might share an amicable friendship, or two amiable people might end their relationship amicably.
Both amiable and amicable derive ultimately from the Latin amicabilis, meaning friendly. Amiable came to English from French in the 14th century and originally bore the sense now associated with amicable. It developed its modern sense shortly thereafter. Amicable entered English in the 16th century, already bearing its modern sense.
Examples
An amiable fellow, Wally committed this historic act on April 14, 2003 quite by accident. [American Spectator]
No one wants to see this fun end, which is why the current labor negotiations are more amicable than they’ve been in the past. [Boston Globe]
He’s amiable in a familiar Midwestern way, his disposition varies between cheerfully earnest and wry, and he uses words like “gosh.” [Wall Street Journal]
Despite the earnest desire of many of the delegates to find an amicable solution to the growing crisis, the stated mission of the conference was doomed from the start. [Washington Post]
The amiable, shambling bears are also diplomats. [Los Angles Times]
But it would appear hopes for an amicable divorce were misguided, as Reid has apparently demanded £6million in their divorce settlement, while Price had planned to give him £700,000. [Metro]