Fiat Creation
The term "fiat creation" arose in discussions about Charles Darwin's Origin of Species, published in 1859. See a Google Ngram of its usage here. (The Ngram also reflects the surge in interest in the mid 20th Century when Seventh Day Adventist beliefs in Young Earth Creationism and Flood Geology began to be espoused by the Protestant mainstream, and by Christadelphians.)
The English word fiat, meaning decree, order, command, proclamation, mandate etc., means "let there be" in Latin: God's first words, "Let there be light!", are "fiat lux" in the Vulgate translation.
The idea of "fiat creation" is that God simply spoke "the word" and its entire truth came into existence — sometimes, but not necessarily, immediately or instantaneously. Some verses, such as Psalm 33:9 (For he spake, and it was done; he commanded, and it stood fast), appear to support this latter view if the creation narrative of Genesis 2:4-25 is not taken literally; but others do not, such as Psalm 68:11, which illustrates the rhetorical force of a less literal reading.
Divine Fiat Interpretation of Genesis
According to this reading of Genesis 1:1 to 2:3 the seven days represent seven occasions in which the Creator speaks. These days may be understood to have been literal days, or they might be part of a literary framework.
Instantaneous Creation
For a distinction between fiat creation and instantaneous creation see at Psalm 148. For a simple "proof text" against the "instantaneous" interpretation see Psalm 33:6-9 and follow the red asterisk from verse 9.
