How do I increase the definition of a picture?

5 years ago, I uploaded this cropped picture to Derpibooru: https://derpibooru.org/images/1405104
However, it was lower definition and I think was much smaller. Then, someone came along and made it higher definition as well as larger. How is this possible?

Maybe the other person simply found an higher-resolution source for making the updated cropped version.

Ways of increasing the definition of a picture without getting an upscale artifacts mess :

Beyond these specific cases, your mileage may vary…

Though for this particular case, >>862946 is so large (vertically), if you simply right-clic>save the Derpibooru’s thumbnail instead of clicking on View or Download, you get an actually smaller version