What is a reason to speak of "open" before defining openness in a metric space? Let $(E,d)$ be a metric space. To define what it means for a subset of $E$ to be open in $E$, it is standard to first introduce sets of the form $\{ x \in E \mid d(y,x) < \delta \}$ where $y \in E$ and $\delta > 0$, calling it an "open" ball, or something alike, centered at $y$ of radius $\delta$. Then one proceeds to define the real sense of openness by saying that a subset $A$ of $E$ is called open in $E$ if and only if for every $y \in A$ there is some "open" ball centered at $y$ that is included in $A$. And then one proves that every "open" ball in $E$ is indeed open in $E$.
With respect to this logical order, it is tempting to say that the adjective "open" preceding "ball" is something meaningless until one proves that an "open" ball is really open. 
So what is a reason to use the word "open" before defining the concept of openness in a metric space?
 A: Consider this as an incremental definition, meaning that the "open ball" (and not "open" ball as eloquently mentioned) is defined first in a more primitive way of "openness" and then more complex open sets are defined with respect to more primitive "open" sets.
The primitive "open ball" is easier and more direct to define, than complex sets and a general concept of "openness"
Note on comment one can use a variation and not use the word "open" for open balls, and use another one, e.g "non-delimited balls" and then at the end, show the equivalence of "non-delimited balls" to "open" balls. 
But this becomes pedantic after a while.
A: But long before you study metric spaces you learn in 7th grade to speak of open intervals and closed intervals and half-open intervals, etc.  And quite likely the only reason for using the term "open" for open sets in topology is that it generalizes the definition of the more special concept that you learned in childhood.
Here's the problem: one learns concrete instances of an idea first and more general forms later.  To escape that is impossible and probably undesirable.
