TITLE: What does the symbol nabla indicate?
QUESTION [33 upvotes]: First up, this question differs from the other ones on this site as I would like to know the isolated meaning of nabla if that makes sense. Meanwhile, other questions might ask what it means in relation to something else. This might be a very stupid question; it's hard to tell when I struggle to understand what it indicates, and thus this might seem very idiotic for a person fully knowledgeable about its meaning.
Now from the document How do the $\nabla x$ and $\nabla \cdot$ notations work?:

Currently I interpret the nabla symbol as a way of turning something into a vector. Is my understanding correct?
Anyway, what is the meaning of it, and why is it used? (Please try and describe it as simple as possible.)
Less important
In case there should exist multiple meanings of this symbol, this is the context:
I stumbled upon this symbol when researching neural networks (C denotes the cost function):
"-∇C(...)= [*this is a vector of weights and biases*]"  (source)

REPLY [2 votes]: $∇$ is an operator, which takes a scalar function $f$ and turns it into a vector $∇f$ pointing to the direction in which $f$ increases.
Example: in physics you have scalar fields. The temperature is a scalar field: it is a scalar value that varies depending on the position in your room. Apply the $∇$ operator and for every position in your room, you will have a vector pointing in the warmer direction. In winter, all the vector will usually point in the direction of the main heat source of your room: your radiator.