Does limit means replacing $x$ for a number? I don't understand limit so much. For example I see $\lim_{x \to -3}$. And I always just put $-3$ everywhere I see $x$. I feel like I'm doing something wrong, but it seems correct all the time.

Let's go back to the $\epsilon,\delta$ definition of a limit.
Let a function $f$ be defined on an open interval containing the real number $c$. -This mean we aren't going to do silly things like take the square root of negative numbers etc. IN some interval around $c$.
Let $L$ be a real number -Self explanatory.
Then $\lim_{x\rightarrow c}f(x)=L$ if and only if -This is about to be an equivalent statement to what comes next.
For any real number $\epsilon>0$ -So we're allowing $\epsilon$ to be as absolutely small as we like, as long as it's still positive.
There exists a real number $\delta$ with the following property -Ready for this?
For all $x$ if $0<|x-c|<\delta$ then $|f(x)-L|<\epsilon$ -This means that if $|x-c|$ (think of this as the distance between $x$ and $c$) is less than our number $\delta$ then $f(x)$ is arbitrarily close to the real number $L$.
I'm not sure if this was very helpful but let me end by suggesting that you look up visual representations of the above as well as visuals of where a limit does not exist.
