An exhibition for things is put in a public building for anyone to see. This place is a museum.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.
"How was your museum date yesterday, Salmon?" "Horrible!" "Why? What happened?" "Fugu was checking out other girls the whole time! I got pissed off."