The preceding image take form Matthias Weber's Classical Minimal Surfaces in Euclidean Space by Examples notes is called the sphere with three ends. But what does it have to do with a sphere and why do we say it has three ends? What is formally the end of a surface?
Math people, like many other people, tend to use heavy slang, about as cryptic as criminal argot at its worst. Luckily for us, they usually leave behind a trail of definitions which theoretically can be followed.
This surface has nothing to do with a sphere, except that it is a minimal surface (which a sphere is not), and hence can be made of soap film, much like a soap bubble, which is a sphere. Unlike a bubble, though, it has got to have borders. Imagine a weirdly bent soap film stretched on a few pieces of wire. (These, BTW, are the ends of the surface; for more formal definition look here).
So it goes.