'Sub-creation' was used to describe the creative efforts of the Ainur, Elves, Dwarves, and the race of Men (including Hobbits), all of whom are themselves creations by Eru Ilúvatar or in the case of the Dwarves, by the Vala Aulë and given life by Eru. It is called 'sub-creation' because original creation is the province of Eru alone, and that which is made by those created by Eru is derivative from the works of the One.
A notable example of sub-creation and its limitations is Morgoth's efforts to produce the races of Orcs and Trolls. Unable to duplicate true creation, Morgoth instead corrupted or emulated beings already in existence. Orcs were produced from corrupted Elves, while Trolls were said to have been made in mockery of the Ents using the element of stone. Morgoth was not able to simply bring new beings into existence but had to use resources that already existed in Arda.
'Sub-creation' was also used by J.R.R. Tolkien to refer the to process of world-building and creating myths. In this context, a human author is a 'little maker' creating his own world as a sub-set within God's primary creation. Like the beings of Middle-earth, Tolkien saw his works as mere emulation of the true creation performed by God.