What is , it is heavily depends on context.


The reason is that , taken as is, is not a single function or a single value.


 has, strongly speaking, two values, 2 and -2.


 as a function,  has, strongly speaking, two branches,  |  |  and  -|  |.  


In other words, there are TWO different functions practically under the same name.


So, without the context,    is not a single value or a function. 
In opposite, it is THE SET of two values or two functions.


Only if and when the context is EXPLICITLY (or IMPLICITLY) DEFINED, it becomes one function or one single value.


Professional mathematicians "feel" the context practically with no error, but for the school people (students or/and teachers) 
it is often difficult to feel the context.


Therefore in school Math nobody and never explains it, because this understanding gains only with experience.