When people refer to Gower nowadays, they almost always mean the peninsula lying to the west of Swansea, or sometimes more specifically to the Gower Area of Outstanding Natural Beauty.
Gower, however, is much bigger than either of these and encompasses the ancient lordship of Gower, which itself was based on the earlier Welsh commote known as Gŵyr. The boundaries of most early territories are made up of natural features, and Gower is bounded by four rivers; to the west is the river Loughor, to the east, the Tawe and to the north the Amman and the Twrch. The manor of Kilvey, to the east of the Tawe is usually attached to the lordship. In modern terms, the lordship of Gower is more or less the area of the City and County of Swansea.
(Sometimes people talk about The Gower - but remember that it is just Gower.)