At least some content in this article is derived from information featured in Fantastic Beasts and Where to Find Them (film). As such, spoilers will be present within the article.
Magizoologist Newton Scamander owned a magical suitcase, bewitched with an Undetectable Extension Charm, in which he held a number of beasts while he travelled. He could hide the contents from Muggles by flipping a switch on the case.
In 1926, whilst visiting the United States of America, the beasts in Newt's suitcase escaped, whereupon he was accosted by Percival Graves, a powerful MACUSA Auror and right-hand man of the American wizarding community's leader, Seraphina Picquery.
The suitcase contains it's own world with many different habitats for each creature. It also contains a place for Newt.