"The boy goes around the library."
Translation:Téann an buachaill timpeall na leabharlainne.
An leabharlann is the nominative singular which you could use in a sentence like "Téann an buachaill go dtí an leabharlann" [The boy goes to the library].
Na leabharlainne is the genitive singular which is used in this sentence because it follows the preposition timpeall which is one of several that require use of the genitive case.
I don't know if I'm reading too much into things or if knowing the answer to this will help my understanding in any way, but here it goes.
I noticed that bialainne and leabharlainne end the same way. Is lainne a word on its own? Building or somesuch? Is it a suffix and not a word at all? Any help would be appreciated if it will help me learn.
bialainne is the genitive of bialann, leabharlainne is the genitive of leabharlann.
lann can mean "Land, ground, site. Building, house; church". Aside from bialann and leabharlann, you might have encountered pictiúrlann, grúdlann, dánlann and amharclann on Duolingo, along with lots of references to teanglann.ie,
Other examples are otharlann - "infirmary", ceardlann - "workshop", bearblann - "barber's shop", beachlann - "apiary", marglann - "mart", feithealann - "waiting-room", armlann - "armoury", léachtlann - "lecture theatre".