One-line summary

Convert one interface into another the client expects — letting classes work together that couldn't otherwise because of incompatible interfaces.

When to use this skill

Integrating a third-party library that has a different interface than what your code expects.
Migrating from an old API to a new one — write an adapter that exposes the old interface in terms of the new (or vice versa) and switch incrementally.
Two systems must talk and you can't change either — adapter sits between them.
The classic Adapter example: an electrical plug adapter that lets a US plug fit a European socket; the underlying current is the same, only the interface differs.

The two interfaces serve genuinely different conceptual purposes — an adapter would be doing translation work that hides a real domain decision; surface the decision instead.
Only one method needs adapting and the host class can change to call the source directly — adapter is overkill.
The wrapper adds behavior rather than changes interface — that's gof-decorator.
The wrapper hides complexity of a subsystem — that's gof-facade.