What is this web on the surface of the Sun? I was going through my Social Media Feed and found the attached post too frequent. The caption reads this is the best image of our Sun. Just as an example, the Universe Today's This is the Highest Resolution Image Ever Taken of the Surface of the Sun

Why? What exactly are the black lines that appear to be like kind of a web, and will such patterns be observed if in case the star was not the Sun but some other star? Are they thought to be common?
The dark lines are colder areas at the edge of the convection cells, where the cooled down plasma sinks towards the inside of the Sun. Now "colder" for the surface of the Sun, is still pretty hot, as explained here. 

The yellow parts are where the plasma rises to the surface. 
Each yellow spot (which is actually the size of a country) is called a granule, and this web-like appearance is called granulation. 

In the outer part of the Sun (the convection zone in the image below), there is convection, that is hotter plasma floats towards the top, cools down at the surface, and sinks back down, like in a lavalamp. 



The existence of a convective zone in the outer part of the star is determined by the mass of the star, and all stars with a convective zone in their upper layer are thought to have such granulation patterns. So stars like our sun, or smaller have these patterns. 

For larger stars, though, the convective zone is in the inner part of the star, and the outer part of the star is the radiative zone, so there might not be the same patterns on the surface.