I am so confused about the terminology and vocabulary here. I tried googling it but couldn't find anything satisfactory. I have a test tomorrow. I would be glad if someone could explain what this conceptually means.
I'm guessing you're currently in high school so without beating around the bush and/or being pedantic and asking you for definitions (which is futile as it is obvious you have this question because you don't know your definitions in the first place) and since you have an exam coming up very soon, I'll give you a straight answer.
$f(x)$ simply means the output value using the function $f$ when $x$ is the input value. For example: $f(x)=2x+3$ then for input value $x=2$, the output value using the function $f$ is $f(2)=2(2)+3=7$. You'd usually (conventionally) want to plot these output values of function $f$ on $Y$ axis and input values on $X$ axis on a graph paper. So we set $y = f(x)$. And hence, now $y$ is simply another name for $f(x)$.