Before wizards went underground, when we were still being hunted by Muggles, young wizards and witches sometimes tried to suppress their magic to avoid persecution. Instead of learning to harness or to control their powers, they developed what was called an Obscurus.
-- Newt Scamander (WFT)
An Obscurus is a powerful Dark force that develops inside a young witch or wizard who has to constantly repress or hide their magical abilities (WFT). The children who develop an Obscurus have lived through some kind of trauma associated with magic, which creates shame and the attempt to suppress their abilities on a regular basis (JKR).
When an Obscurus force becomes active inside a young witch or wizard, it appears to crawl under the skin until it finally takes over the host and becomes a Dark mass in which the human face only appears sporadically. It has the ability to fly, dodge spells, destroy objects, and becomes an “unstoppable kinetic mass.” When separated from a human Obscurial, the Obscurus appears as a “small, oleaginous black mass” which at times becomes more active, “pulsing, swirling, and hissing” with energy. Newt Scamander kept one for study after trying and failing to save the life of an 8-year-old Obscurial witch in Sudan.
Once separated from the “host” child, an Obscurus poses no danger to anyone according to Newt Scamander. However, he warned his No-Maj friend Jacob not to touch the one in his suitcase (WFT).
When the Obscurus of Credence Barebone was destroyed by Aurors, it left behind only “small tatters of black matter …floating through the air like feathers” (WFT). This small bit of black matter reformed into Credence who then escaped to Paris with the Circus Arcanus (CG).
History and Notes
Latin "Obscurus" = "Dark"
The publisher of Newt Scamander's book Fantastic Beasts and Where to Find Them is called Obscurus Books. It is unclear what connection this has to Obscurials, although we know that Newt had an interest in saving children from them.
J.K. Rowling made it clear on Twitter that an Obscurus is something magical, and not a creature, even though it is called a "parasitical force" in the Fantastic Beasts script:
An Obscurus isn't a creature... https://t.co/O3bsc4ObZ5
— J.K. Rowling (@jk_rowling) January 5, 2017
On the newest version of Rowling's website, she explained why Harry Potter never developed an Obscurus inside him even though he was expected to suppress his magic while at home on Privet Drive:
The Dursleys were too frightened of magic ever to acknowledge its existence to Harry. While Vernon and Petunia had a confused hope that if they were nasty enough to Harry his strange abilities might somehow evaporate, they never taught him to be ashamed or afraid of magic. Even when he was scolded for ‘making things happen’, he didn’t make any attempt to suppress his true nature, nor did he ever imagine that he had the power to do so (JKR).