What is a supremum? I'm reading here about sequence of functions in Calculus II book, 
and there's a theorem that says:

A sequence of functions $\{f_n(x)\}_0^\infty$ converges uniformly to $f(x)$ in domain $D$ $\iff$  $\lim_{n \to \infty} \sup_{x \in D} |f_n(x) - f(x)| = 0.$

I really serached a lot , in Google, Wikipedia and Youtube,
And I'm still having difficulties to understand what is sup.
I'll be glad if you can explain me. thanks in advance!

supremum means the least upper bound. Let $S$ be a subset of $\mathbb{R}$
$$
x = \sup(S) \iff ~ x \geq y~\forall y \in S \mbox{ and } \forall \varepsilon > 0, x - \varepsilon \mbox{ is not an upper bound of } S
$$
You may also define $\sup(S) = +\infty$ when $S$ is not bounded above.
The reason why we have supremum instead of simply maximum is that in some subset of $\mathbb{R}$, we do not have maximum element, let's take an open interval $(0,1)$ as an example, $\max\{(0,1)\}$ does not exist, but $\sup\{(0,1)\} = 1$. 
Supremum of a nonempty subset having an upper bound always exists by the completeness property of the real numbers.
