Literally 'picture-house'. You might have noticed that the suffix '-lann' is used with lots of words for buildings were you can get something or some service. And every word ending in -lann is feminine.
I didn't try it, but does anyone know if theater is allowed here as well as cinema?
"Movie theatre/theater" would be accepted, but "theatre/theater" would not. The word for a theatre where plays, musicals etc are staged is amharclann (literally "viewing house").
In the US, we usually say just theater instead of movie theater. It sometimes requires context to know what kind of theater. Still, I've gotten the impression that Duo tries to support both British and American.
When I saw this word in the list of upcoming words, I thought it would turn out to be an art gallery.
In Ireland, (older?) people still say "I went to the pictures last week" where Americans might say "I went to the movies" (though as in many aspects of informal speech around entertainment, the American usage is increasingly prevalent, and younger people are probably more likely to say "movies", but they'd still recognize "pictures" in this context). There was a similar usage in the US - the title of the 1971 film "The Last Picture Show", and the term "Picture House" (which is pretty much what pictiúrlann means) is still used in the UK as the name of a chain of cinemas. (Wikipedia redirects Picturehouse to "Movie Theater").
Also, "Rocky Horror Picture Show"! It is rather interesting how you can perhaps discern different patterns of thinking about the phaenomenon: the "movie" focuses more on the action, changing of the pictures, the "picture (show)" on the fact that the art's focus is on watching the picture(s), and the "film" I would say on the way it is made, by camera and photography/cinematography. Just my two cents.