Newton 'Newt' Scamander owned a magical briefcase, bewitched with an Undetectable Extension Charm, in which he housed a vast number of magical beasts while he travelled. He could hide the contents from Muggles by flipping a switch on the case.

This case accompanied him to New York City in 1926. During this time, several of his beasts escaped by accident and wreaked havoc across the city.

In 1926, Newt Scamander took the case with him to New York City, where he was supposed to briefly stop before a trip to Arizona to release his Thunderbird, Frank, into the wild. Upon arrival, the case was inspected by muggle border control workers. Seeing one of the latches was flicked open (presumably by the Niffler), Scamander ensured the case was set to its 'Muggle-Worthy' setting, which displayed his clothes and goods to the boarding patrol guard rather than the beasts he cared for.

When Scamander stopped in front of the Steen National Bank to listen to one of Mary Lou Barebone's speeches, the Niffler managed to escape the case and run into the bank, where it attempted to steal valuables from the vaults. The Niffler was swiftly returned to the case by Newt.

When Newt Scamander, aided by ex-Auror Porpentina 'Tina' Goldstein, arrived to retrieve the case, he discovered an injured and confused Kowalski. Helping Kowalski to his feet, Goldstein took the duo to her apartment. After a meal, when Kowalski and Scamander lay in beds provided by Porpentina and her sister, Queenie, Scamander opened the case and invited Kowalski inside, so that he could assess which of his creatures managed to escape.

Inside, the two of them took care of the jobs that needed doing, including feeding the Mooncalves and a Marmite.

Scamander, guided by Kowalski, took the case with him to secure the escaped creatures. At a jewelry store, Scamander captured the Niffler, who was safely returned to the case. Soon afterward the Erumpent was discovered in the Central Park Zoo. This immense beast proved difficult to return to the case, mostly due to its large size and increasing desire to mate with Kowalski (who had accidentally covered himself in Erumpent musk), although it too was safely returned.

Tina, annoyed that Scamander and Kowalski deserted her, tracked them down and captured them inside the case by locking it while they were inside. She swiftly presented the case to Seraphina Picquery, who after hearing that the case contained a detached Obscurial, ordered the arrest of the trio and seizing of the case by Percival Graves (mass-murderer Gellert Grindelwald in disguise). However, Queenie was able to help Kowalski escape imprisonment and steal the case back, which she used to hide Kowalski, her sister, and Scamander during their escape from the ministry.

The case was taken to a department store in order to capture Dougal, the escaped Demiguise, and the baby Occamy that Dougal was babysitting. Dougal let himself be captured easily knowing Newt's harmless intentions and liking life inside the case, but the young Occamy (possibly the one that was hatched at the bank) provided a challenge. After shrinking it inside of a teapot by temptation of a cockroach, Scamander, Kowalski, and the Goldstein sisters headed inside of the case where they take care of the creatures (it is presumed that the escaped Billywigs were either captured off-screen, or Newt either forgot about them (at some point he was aware that one had escaped) or simply let them escape, due to them being too fast, small, and safe to cause harm or destruction.

Scamander, attempting to subdue a raging Obscurial named Credence Barebone, hands the case to Tina, who gave it to her sister after chasing after Newt. After Credence was seemingly killed and Graves was captured and revealed to be the Dark Wizard Gellert Grindelwald in disguise, Newt was tasked with Obliviating the non-magical citizens of New York, who were now aware that wizardkind and magic exist. Scamander, who had previously wanted to release Frank - his Thunderbird - in Arizona, set him free here, where he flew into a brewing storm which he contaminated with diluted Swooping Evil venom. The rain (which was given powerful Obliviatory properties due to the venom) washed away their negative memories of magic, successfully managing to keep the American wizarding world secret from the No-Maj world.

After saying goodbye to Jacob, Tina, and Queenie, Scamander boarded a boat back to England and took his case with him.

Newt's briefcase was an old, brown, leather briefcase with Muggle-Worthy switches to hide the contents from Muggles. It was made sometime before 1926.

Inside was a magically vastly expanded world where Newt housed his many creatures. The beasts were often then released back into their natural habitats once Newt deemed them fit enough to survive on their own.

However, the case held a switch labeled 'Muggle-Worthy'. When flicked, it transformed back into a regular briefcase. As a regular case, it contained clothes, a tour brochure, a compass, a Hufflepuff scarf, gloves, a magnifying glass, a map, and binoculars amongst other things.

Magical Interior
The briefcase contained its own magically expanded world with many different Atmospheric Charms placed to sustain a number of different habitats for each creature. It also contained a shed for Newt. Newt's shed had a picture of Leta Lestrange, his notebooks, Beast codes, a copy of Bestiarium Magicum, plants, Beak Balm, Shell Shiner, and other Magizoology books.

There were many habitats within the case specially constructed for each of the various creatures that Scamander kept inside:

Creatures Contained In the Briefcase
This is a list of creatures known to have been contained within the suitcase at one point or another: Source: Fandom