Eryri, Snowdonia in English, was the place in Gwynedd to which the Princes of Wales retreated, and their final stronghold when the English pressed on them from every side. Mt. Snowdon (Yr Wyddfa) has always been at its center, but it traditionally included the Carneddau range and essentially all the land west of the Conwy River. It is the land the Edward allowed Llywelyn ap Gruffydd to keep in the 1277 treaty. Today, as a national park, it includes 838 square miles.
From John T Koch, Celtic Culture: An Historical Encyclopedia:
“The first literary mention of Eryri occurs in the 9th century Historia Brittonum, where an account is given of the downfall of the semi-legendary 5th century king Vortigern. Pursued by his revolted Anglo-Saxon mercenaries and hated by his Brythonic countrymen, the king’s magi direct him to build a stronghold in a secure place on the far side of his kingdom. Such a place is found in Eryri . . .
“The place-name Eryri has had two Celtic roots proposed to explain it: 1) that it describes a high place [from the Latin eryr] or 2) that it denotes the abode of eagles [Welsh eryr 'eagle']. Of course, even if Eryri had not originally meant ‘eyrie’, this idea would automatically occur to any Welsh speaker, writer, or poet . . . In a transferred sense, eryr is often used as a kenning for ‘hero’ in Welsh poetry, which adds further significance to the place-name as the traditional mountain stronghold of the strongest and most militaristic independent Welsh kingdom, Gwynedd.”
1262 marks the year that Llywelyn ap Gruffydd styled himself for the first time as “Prince of Wales and Lord of Snowdon (Eryri)”. Llywelyn Fawr had referred to himself as ‘prince of Aberffraw’, which his grandson no longer mentions, although others continue to refer to him as its lord (J. Beverly Smith Llywelyn ap Gruffydd p. 145). Because the latter was never recognized by the kings of England, the second Llywelyn chose to focus on Wales instead of Aberffraw Both, however, were ‘lord of Snowdon’ and believed that this land encompassed not only Eryri as present historians have come to know it, but to all the lands in Gwynedd from the Dee to the Dyfi Rivers (Smith, p. 188).