Galicia is an autonomous community within Spain with its own regional government (the Xunta de Galicia) and its own language, Gallego, which is the principal language for most schools in Galicia (with Castellano, which is what they call Spanish in Spain, also taught as a first language).
What is Gallego?
Gallego is considerably more than just a dialect but is generally (unlike Basque, for example) just about comprehensible to a Spanish speaker, and especially so if they also speak Portugese as much of Gallego is a mix of the two.
Recent history of Gallego
Gallego was banned in favour of Castellano (ie. Spanish) by the dictator Franco, who was actually from the Galician city of Ferrol. Old folk here tell of signs on the buses which used to read (without any humourous intent) “No spitting, no swearing, no Gallego”!
The brutal repression of what was basically a native language gave rise to strenuous attempts to reintroduce Gallego when Galicia become an autonomous community in post-Franco democratic Spain, and although the Spanish constitution enforces the right to be able to speak and deal with authority in Spanish throughout Spain Gallego is also recognised as an official language in Galicia and official correspondence tends to arrive in Gallego unless you specifically request otherwise.
Speaking Castellano (Spanish) in Galicia
As post-Franco education has always included Spanish (Castellano), in theory everyone in Galicia should be able to speak Spanish.
In practice this is true in the cities and amongst younger and more educated people, but in country villages it is common for people, intentionally or otherwise, to speak only Gallego.
If you speak Spanish adequately you should be understood anywhere in Galicia even if you sometimes don’t understand the reply, which will normally be delivered in an extremely loud voice as there seems to be a common misconception, especially in rural areas, that this helps foreigners understand.
Speaking English in Galicia
If you come to live in Galicia then you need to be aware that you cannot get by with only English (or any other European language other than perhaps Portugese) in Galicia. Although English is a compulsory subject for many years in school it seems to be taught in such a way that most Galicians have no confidence speaking it and so rapidly forget what they have learned after they leave school.
You will also find that absolutely all TV and film media is dubbed in Spain, and when I last looked there wasn’t a single original language film showing in all of Galicia. Fortunately with the arrival of digital TV English audio is now available on most English language TV programs.