What's the point of "created limits"? Seeing as there's an nLab page about creation of limits, I take it that at least some people think this is an important notion. There's also a discussion here about what the "correct" definition of this notion is. However, and maybe this is just my ignorance speaking, but I haven't actually found a reason to worry about this notion, so I basically just ignore it. I mean, okay, a diagram $D$ that lacks a limit in one category $\mathbf{C}$ might gain a limit in a category with more objects, or arrows, or both. More generally, given a functor $F : \mathbf{C} \rightarrow \mathbf{D}$, the composite $F \circ D$ might or might not have a limit, quite independently of whether or not $D$ does. But so what? I don't quite get what the notion "creation of limits" really teaches us.

Question. Can someone who finds this to be a helpful notion explain what they find helpful about it? Is there, for example, a theorem about creation of limits that's ubiquitous but impossible to see without this notion? Is there an important definition that can't be elegantly stated unless creation of limits is invoked? What's the point of this idea?

 A: The main point of “creating limits” is things like:
Theorem. If $C$ has all limits of shape $I$ and $F : D \to C$ creates such limits, then $D$ has all such limits and $F$ preserves and reflects them.
In other words, the definition is pretty much designed to be a tractable and concrete solution to the implication “(limits in $C$) + ???? $\Rightarrow$ (limits in $D$, and preservation/reflection)” 
Pragmatically, it isolates the structure common to the construction/analysis of limits in groups, topological spaces, algebras for monads, and many other categories of “structured objects over some category where limits are already understood”.  It does require constructing the limits in $D$ anyway, but it guides you to a particular tractable way of constructing them, and then shows that by constructing them this way, you get preservation + reflection for free.
Regarding the two different definitions of creation of limits, see Displayed Categories, Ahrens, Lumsdaine 2017, arXiv:1705.04296 for my personal (maybe slightly idiosyncratic) take on why the standard definition using equality of objects really is very reasonable and natural.
A: This is not what "creates limits" means, although I also find this terminology slightly confusing (in the sense that if I had to guess the definition just from the word "creates" my guess would probably have been the same as you, but it's just not that).
The definition (eg the one stated in the nLab page you mention) does require the limit of $D$ to exist in $\mathbf C$ in the first place, but what it says is basically that you can compute it in $\mathbf D$, ie roughly we have both:


*

*$F$ of a limit of $D$, is a limit of $F\circ D$

*somewhat conversely (and imprecisely), if some $F(x)$ happens to be a limit of $F\circ D$, then $x$ was already a limit of $D$.


Now as far as I know this definition is most often used for some shape of diagrams rather than for a single one, and as pointed out in the nlab is used in Beck's monadicity theorem. The main example of that phenomena (the colimit version) is that a direct sum of modules over some algebra is just the direct sum of the underlying vector spaces with the "obvious" module structure.
