The early picture of the cosmos was far from what we know and imagine today. Originating from the Ancient Greeks, the universe was depicted as a finite space with Earth at the centre. In earlier centuries astronomical technology was far simpler than what we have today, and as such many of the beliefs about the universe were based upon religious ideologies developed at the time rather than detailed observations. Galileo played a key role in the transition between natural philosophy and the science behind the universe (1); He pioneered a step away from the idea of Earth as a singular central point of the universe, with his discovery of Jupiter's moons in 1610. He observed four different bodies orbiting the planet with different radii and periods, proving that Earth is not an absolute central point orbited by all objects. The legacy of his ideas continued, and later in the century the idea of the Sun being at the centre of the Solar system was confirmed by both Newton and Kepler with their discoveries of planetary motion and the laws of gravity respectively (2).
Knowledge had progressed from a central Earth Universe, to the Sun being at the centre. However, the idea that the Milky Way was all that existed in our finite universe remained. In later centuries the 'Island Universe Theory' was hypothesised, claiming that the milky way galaxy was one island, with many other distant island (galaxies) forming a much larger universe. It wasn't until the early 20th Century that this idea became under advanced scrutiny by a number of astronomers. In 1917 Heber Curtis was observing novae within a 'spiral nebula' in the night sky, and estimated their distances using measurements of apparent magnitude to be significantly further away than other observable objects within the Milky Way (3). The nature of a nova (a star that suddenly increases in brightness) made the measurements possible with the lower power telescopes of the time period. The significantly larger distance of the objects that were observable supported the Island Universe Theory because it suggested they were too far away to be a part of the Milky Way galaxy. Just under a decade later in 1925, Edwin Hubble was able to accurately measure the distances to specific stars in the same spiral nebula known as 'Cepheid Variables'. These pulsating stars have a strong relationship between the period of pulsation and their absolute magnitudes. As such by measuring their differences in apparent magnitude, it is possible to calculate distances to the object accurately. These accurately measured distances to 40 different Cepheid Variables that he had located, were once again much larger than distances within our own galaxy and supported the Island Universe Theory, which was finally accepted by astronomers (1). The 'spiral nebula' was actually the Andromeda galaxy, the closest neighbour to the Milky Way.
Looking back through the 20th Century, it is clear to see that Hubble's discovery accelerated the progression of astronomical equipment. An example can be seen in the case of reflector telescopes. The primary mirrors of these instruments saw increase in diameter from 2.5m in 1918 (Hooker telescope as used by Hubble) to 9.8m (Keck 1 and Keck 2 telescopes) by the end of the century (3). As such the power of such telescopes increased massively over the century. Moreover, telescopes were further developed to detect wavelengths outside of the visible spectrum, with the first example being a creation by engineer Karl Jansky in 1931 (5). More and more examples would be developed up until present day. As well as this, we can see advances in their locations, with the famous 'Hubble telescope' (named after Edwin Hubble himself) becoming the first telescope to be placed outside of the Earth's atmosphere with its' launch in 1990 (4). In my opinion Hubble's discovery was the main factor in the acceleration of this progression. This is because the known boundaries of our universe were vastly increased by the known existence of other galaxies and therefore there became a need to develop more powerful telescopes in order to search further away from our own galaxy.
In addition to advances in technology, the need for scientists in the field of astronomy increased. This is because changes to our understanding of the structure of the universe were so drastic that it opened up the ability to study our universe further. Due to a higher number of astronomers initiated in my opinion by Hubble's discovery, more knowledge and understanding would be gained in this century than any other.
The 'Big Bang' Theory is generally accepted today by most cosmologists and suggests that the universe is expanding. A key piece of evidence that supports this is 'Hubble's law'. Hubble's law states that bodies in the universe are moving away from each other, and the relative velocity of this increases linearly with separation from the respective bodies, thus the universe is expanding. This was found by observing the Doppler shift of different galaxies. Doppler shift to bodies within the Milky Way would show no meaning towards an expanding universe theory, only Doppler shift from bodies further afield are relevant (the Doppler shift from the Milky Way and other distant galaxies). The knowledge of universe structure is key to this argument, and without the prior discovery by Hubble, this key piece of evidence to support the Big Bang theory would not have been possible.
In conclusion, I believe that the discovery of other galaxies by Edwin Hubble in 1925 is the most significant finding in cosmology. The nature of the finding was such that the sandpit for further astronomical discoveries was vastly increased, and this lead to huge advancements in technology and knowledge. Furthermore, Hubble was able to use this knowledge he had acquired in order to provide a key piece of evidence to answer one of the most wondered questions: What is the origin of our universe? Hubble's discovery does add additional mystery to the world of cosmology though. Through history scientists have been obsessed with ourselves as being a central figure; First our planet, then our star, then our galaxy, and now our universe. Are we looking too narrow once again, and there is a larger and more puzzling body such as a 'multiverse'. An answer to this seems very far away, but the curiosity of cosmologists will continue to tick with time.