The abundance of oxygen in the universe is a consequence of the inner workings of stars. Stars are, in a way, elemental factories, taking light elements like hydrogen and helium and fusing them together to form all the elements ranging up to iron. Some stars explode, and their explosion creates elements heavier than iron.

The reason why oxygen is so abundant is not totally understood, but one current idea involves the fact that massive stars (stars more than 1.3 times the mass of the sun) reach a stage in their life where they make helium from hydrogen using a process called the carbon-nitrogen-oxygen (CNO) cycle. Late in this stage the stars stop burning hydrogen to make helium and instead burn helium to make heavier elements, like carbon, nitrogen, and oxygen. Why oxygen is more abundant than carbon and nitrogen is not totally clear.

This answer is a bit vague because I'm no cosmologist and not a lot of people are astute enough to ask such a difficult question. However, I hope this answer gives you some sense of the forces at play in making oxygen #3 by mass in the universe.

That's a good question because it totally seems like the abundance of elements might drop off as you increase in atomic number, but yet there's more oxygen than there is lithium, beryllium, boron, carbon or nitrogen, which are all smaller elements.

During the big bang, mostly hydrogen and helium were produced, and most of the heavier elements are formed inside of stars in a process called nuclear fusion, meaning that the nuclei of multiple atoms are combined to form a new atom. In addition to the heavier elements, stars also continue to form more helium by fusing 2 hydrogen nuclei.

So there's lots of helium around in general and there is a process called a triple-alpha process by which 3 helium atoms can come together to form carbon. Importantly, this process forms a stable carbon-12 isotope, whereas the combination of only 2 helium atoms forms an unstable beryllium-8 isotope, which then quickly decomposes. This is why there's not much beryllium, but considerably more carbon. Carbon then participates in further fusion reactions, including the fusion with another helium atom to form oxygen-16, which is also very stable. Carbon is consumed in the process, and this is why we end up with slightly more oxygen than carbon and considerably more of both oxygen and carbon than most other elements.

The smaller atoms, which are not preferred by nuclear fusion (such as beryllium) may be formed by decomposition of some isotopes of larger elements.