In 1929 Edwin Hubble published his observations of the redshift and distances of nearby galaxies. Hubble observed in the light from most of those galaxies that the spectral lines were shifted towards the red end of the spectrum as compared to a local laboratory source of the same atomic gas species. From this he interpreted that it was a Doppler effect (ie. due to the motion of the source), where the galaxies were receding from us, the observer. Thus the idea of the expanding universe was founded.
But one other important idea came from those same observations. He observed roughly the same redshift in light from the galaxies as a function of distance in every direction he looked. This became known as the Hubble law, which is the basis for the standard cosmology today–the big bang model. But the fact that this was in every direction and that the proportionality between the redshift and distance was the same in every direction meant that it looked to him like we, that is, our galaxy, was at the centre of the Universe. This is because the galaxies were moving away in a spherically symmetric way, putting us at the centre. This view of the Universe then would look something like the image in the figure on the right.
“Such a condition would imply that we occupy a unique position in the universe, …. But the unwelcome supposition of a favored location must be avoided at all costs…. is intolerable; moreover, it represents a discrepancy with the theory because the theory postulates homogeneity.” [emphasis added] pp. 50-59
But Hubble could not believe his own observations because of his bias. This is because he was an atheist and believed the universe was the result of natural forces and not the work of a Creator God. To him the obvious conclusion must be avoided. This highlights the problem of cosmology. It is not the evidence that determines the true structure and history but it depends on the worldview, or religious view, of the researcher. It is within that framework Hubble interpreted his observations.
Hubble thought intolerable the idea that our Galaxy might occupy a special position in the Universe. To him it was intolerable because the theory, which is the standard big bang model (of Friedmann and Lemaître), requires homogeneity and isotropy. This means the mathematics of the big bang model is only valid if the distribution of the galaxies is the same in every direction and uniform for any observer at the same epoch of time. But note this is the principle assumption of the big bang, called the Cosmological Principle.
So essentially he is saying that from his observations it appears that we are located at the centre of the Universe, but that conclusion represents a discrepancy with the theory because he believes the theory despite his observations. The theory says the Universe is the same everywhere. It must be right, therefore there must be another interpretation. His believes the theory is correct, so how can he make the observations fit the theory. He has no faith in the biblical Creation. That can’t be right. There must be another solution.
And the solution to his dilemma is curvature. This is curvature of space, that he is talking about. The image on the right illustrates this. The mass/energy content of the Universe determines the curvature of the space within it. If the Universe has critical density (Ω0= 1) it has Euclidean geometry, which we are all familiar with, but if has greater density (Ω0> 1) its geometry is curved and closed in on itself like a finite sized sphere (right top image) and if it is less than critical (Ω0< 1) its geometry is curved out and infinite (right middle image). This illustration shows 2D surfaces which really represent 3D spaces. See here for more detail.
“Therefore, in order to restore homogeneity, and to escape the horror of a unique position, the departures from uniformity, which are introduced by the recession factors, must be compensated by the second term representing the effects of spatial curvature.” [emphasis added] p. 59
And as a result we have the standard big bang model today with all its unknowns that are needed to make sure the theory fits the observational data. In any lab experiment it would be discarded, but because the only alternative is the creation by an intelligent Creator, which according to Hubble is intolerable, that cannot be permitted.