He apparently visited Galicia several times, and in 1932 spent part of the summer there with his travelling theatre company. This was when the poems were written, and they were published in 1935 with a preface by Blanco-Amor under the (highly imaginative!) title of Seis Poemas Galegos. [Poema is one of those peculiar words that ends in 'a' and yet is masculine.]
It's a little-known part of his output; many selections of his poetry do not even mention it. Of course, this is not very surprising: few Spaniards bother to learn Galician, let alone anyone else. It's something the Galicians though are rather proud of. A 400-page book O Pórtico Poético dos Seis Poemas Galegos de Federico García Lorca, discussing the history and presenting the text of the poems, together with various other things such as a setting to music by Isidro Maiztegui Perreiro, is available for free download from the Consello da Cultura Galega site (warning! 13.6MB). The full text of the poems is available as html pages on Eric Laermans' site.
Of the six poems, one is about Bos Aires (Buenos Aires), often jokingly called the largest Galician town because of the large number of Galician emigrants who live there (who, incidentally, even have several websites, for example, here). One is a tribute to Galicia's most famous poet Rosalía de Castro. Two of the poems are about Santiago but, whilst there is one about the pilgrimage to Muxía - Romaxe de Nosa Señora da Barca - it was obviously not the pilgrimage that impressed Lorca about Santiago, but the weather. Indeed, the weather in Santiago bears little resemblance to that of Lorca's beloved Andalucia.
I first came across the work via one of my favourite Galician folk bands, Luar na Lubre, who sang a setting by Alberto Gambino of one of the poems on their 1999 album Cabo do Mundo (also on their 15th anniversary album). The sleeve notes said 'Words by Federico García Lorca', but the idea of the Troubadour of the South writing in Galician seemed so unlikely I assumed this was something they had translated themselves from Castilian. But on investigating further I found out about the Seis Poemas Galegos. Luar na Lubre called the song after its first line 'Chove en Santiago' (It's raining in Santiago), though Lorca actually entitled his poem Madrigal á Cibda de Santiago. 'Cibda' had me puzzled for a while; it's not in my Galician dictionary. But then I realized it was 'civita', 'city': so 'Madrigal to the City of Santiago'. It contains the memorable line 'Santiago, lonxe do sol', 'Santiago, far from the sun' - come on, Federico García, it's not that bad! There's an English translation of the poem on Tony Kline's site. And if you're interested in Luar na Lubre's version, the sheetmusic is also available as jpegs on their website.
The other poem on Santiago is called Danza de Lúa en Santiago (Moon Dance in Santiago), which is also translated on Tony Kline's site, as is the final poem of the six, the sombre Noiturnio do Adoescente Morto, Nocturne of the Dead Youth. The Danza de Lúa, with its talk of wolves and melancholic oxen in the courtyard of the dead, is definitely the stuff of Galician folk legend, something Lorca will have been very interested in. Is the 'quintana dos mortos' a reference to Compostela's history as a cemetery, I wonder? One presumes this is not the sort of thing the Santiago tourist office would want you to associate with the city. Will they produce anything this year for the 70th anniversary of the publication of the work, I wonder?