Can someone explain in general what a central difference formula is and what it is used for? Topic- Numerical Approximations

Even though I feel like this question needs some improvement, I'm going to give a short answer.
We use finite difference (such as central difference) methods to approximate derivatives, which in turn usually are used to solve differential equation (approximately).
Recall one definition of the derivative is
$$f'(x)=\lim\limits_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h} $$
this means that
$$f'(x)\approx\frac{f(x+h)-f(x)}{h} $$
when $h$ is a very small real number. This is usually called the forward difference approximation. The reason for the word forward is that we use the two function values of the points $x$ and the next, a step forward, $x+h$. Similarly, we can approximate derivatives using a point as the central point, i.e. if $x$ is our central point we use $x-h$ and $x+h$. The central difference approximation is then
$$f'(x)\approx\frac{f(x+h)-f(x-h)}{2h}.$$
