Translation surfaces are locally flat surfaces and come with an action of $SL(2,\mathbb{R})$. A certain one-parameter subgroup defines the Teichmüller flow in the moduli space of translation surfaces. For infinite translation surfaces of a certain kind (for example when having a wild singularity and the topological type of a Loch Ness monster), the diameter of the surfaces in the Teichmüller orbit goes to zero. This behaviour is called degeneration.
I will define all the words used above, describe the phenomenon of degeneration, and explain why it is bothering me so much currently.