Imagine if given an amino acid sequence, you could quickly calculate what the shape of the corresponding protein would be.
- You would be able to predict what effect a mutation would have on the shape of the protein. Switching just one glutamic acid with valine completely changes the shape of hemoglobin to the extent that people with this mutation are said to have a disease called "sickle cell anemia". Likewise, there might be a substitution that we haven't even discovered yet that would increase our capacity to inhale oxygen, leading to super-human strength just as the glutamic acid to valine substitution causes can have severe implications (sick cell anemia).
- You could do inverse design. For example if you want a protein that looks and can behave like a stapler, you could search for the amino acid sequence that gives you the protein shaped the way you want, a bit like DNA origami but without the need for staples:

So what did DeepMind announce 2 days ago?
First of all, the link you provided is to an article about what they did. This is the original blog post that DeepMind published 2 days ago.
What they announced was that they did very well in the CASP 14 competition. This is a competition for protein folding predictions that has been going on every two years since 1993 and this is the 14th competition that has taken place. In this competition, researchers try to predict the structure of various proteins, and the predictions are evaluated based on the Global Distance Test. In 2018 DeepMind won the CASP 13 competition with a median score of almost 60 GDT, whereas the winning teams in CASP 7 (2006) to CASP 12 (2016) never got far above 40 GDT.
In the 2020 competition, DeepMind shattered this record again, by getting a median score of 92.4 GDT, which means that atom positions were predicted correctly within 1.6 Angstroms.
Was it peer reviewed?
This was a competition, for which impartial judges evaluate contestants quantitatively based on a single number, the GDP. This is even better than peer review. Peer review for journals, does not involve the referees actually testing the authors' software to see if it reproduces some standard benchmark: it is just a process where scientists guess whether or not they believe that the authors' calculation really did do what they said they did. This competition was a bit like a race, where Usain Bolt was determined by Olympic judges to break the record for the 100m sprint, and non-judges can also believe it because they for the most part saw it happen on TV, just like you can check the results of the 2020 protein folding competition here.
Then why are people saying that they haven't submitted the paper yet?
They won a major competition, so now the authors can get credit for it in the way that is most relevant for their careers as researchers: by publishing in Nature or Science and getting citations on Google Scholar for it. They will likely just report the results of the competition, which we already know. They might reveal some details about any algorithmic developments they made between 2018 and 2020, but they are also a private company and might not reveal everything the way a research institute not owned by a for-profit company sometimes would by institutional policy be required.
So was a "50-year-old problem solved", as they claim?
Not really. The particular benchmark set for CASP 14 was solved to an accuracy that had never been achieved by any research group for any previous CASP benchmark set. However, next time the CASP benchmark set can just be made more difficult and they will be back to not being able to predict the protein structures.
It is however a significant achievement that the protein structures in this benchmark set (which was supposed to be hard by 2020 standards) were reproduced with atom positions correct to about 1.6 Angstroms. It means that scientists can now be that sure about their protein folding predictions for proteins of similar complexity to the ones in the CASP 14 competition set.
Update! After this question, someone else asked a question which pointed out that AlphaFold might struggle for some important types of proteins such hemoglobin, here: Does DeepMind's new protein folding software (AlphaFold) also work well for metalloproteins (proteins with metal cofactors)?