A screaming skull is a human skull which, according to legend, disturbs the house in which it's kept by screaming, speaking, or causing other disturbances. In the case of a few of these skulls, they are the focus of hauntings which stop when the skull is laid to rest – but in the majority of stories, the act of removing the skull from inside the house is what sparks off the trouble.
Sources and further reading:
Westwood, J. and Simpson, J. 2005. The Lore of the Land.
Westwood, J. and Simpson, J. 2008. Haunted England: The Penguin Book of Ghosts.
Clarke, David. 1991. Ghosts and Legends of the Peak District.
Roberts, Andy & Clarke, David. 'Heads and Tales: The Screaming Skulls legends of Britain', in Moore, Steve (ed). (1996) Fortean Studies. Volume 3. John Brown Publishing. London. pp.147-150. In Calvariae Disjecta: The Many Hauntings of Burton Agnes Hall.
Wikipedia - Screaming Skulls, Red Barn Murder, Appley Bridge
'Screaming Skulls', Paranormal Database: http://paranormaldatabase.com/reports/skulls.php
'The Cursed Skull of Tunstead Farm', Ludchurch blog: https://ludchurchmyblog.wordpress.com/places-of-interest-in-cheshire/the-cursed-skull-of-tunstead-farm/
'The Ghost of Ripley's Believe It Or Not Museum', Lancashire Folk: https://lancashirefolk.com/2013/11/27/the-ghost-of-ripleys-believe-it-or-not-museum/
'The Pack Horse Inn History', Affetside Village website: http://affetside.org.uk/pub_history.htm
'Legend of the Screaming Skull', Real British Ghosts: http://www.real-british-ghosts.com/screaming-skull.html