The geocentric theory is a system for describing the universe with Earth-centered coordinates. It was extremely popular from ancient times until the 1600s, as it had better agreement with observation than any alternative. Ptolemy's model was particularly effective at cosmological predictions.
By the 1800s, the spectacular successes of Newtonian theory and Maxwell's equations for electromagnetism had convinced everyone that the Sun is a preferred frame of reference, and that the laws of physics must be applied in that frame. The geocentric theory was considered to be profoundly mistaken, and the heliocentric theory correct.
Since the advent of relativity theory in the early 1900s, the laws of physics have been written in covariant equations, meaning that they are equally valid in any frame. Heliocentric and geocentric theories are both used today, depending on which allows more convenient calculations.
Scripture Quoted to justify Geocentric Theory
A small number of people interpret the Bible as favoring the geocentric theory.
"He has fixed the earth firm, immovable." (1 Chronicles 16:30)
"Thou hast fixed the earth immovable and firm ..." (Psalm 93:1)
"Thou didst fix the earth on its foundation so that it never can be shaken." (Psalm 104:5)
"...who made the earth and fashioned it, and himself fixed it fast..." (Isaiah 45:18)
"The sun also ariseth, and the sun goeth down, and hasteth to his place where he arose." (Ecclesiastes 1:5)
"Then spake Joshua to the LORD in the day when the LORD delivered up the Amorites before the children of Israel, and he said in the sight of Israel, Sun, stand thou still upon Gibeon; and thou, Moon, in the valley of Ajalon. And the sun stood still, and the moon stayed, until the people had avenged themselves upon their enemies. Is not this written in the book of Jasher? So the sun stood still in the midst of heaven, and hasted not to go down about a whole day." (Joshua 10, 12-13)