What is the meaning of $d$? 
What is the meaning of $d$? Is is Delta? If it is Delta, why is it then not $\Delta$? I am still confused with that. Can someone help explain it to me? 
 A: While it's more on the mathematical side, this Wikipedia article should answer your question in more detail (or also here
For physicist, $d/dt$ is the time derivative of a quantity, $\vec{p}$ in your case. So what your formula says is that "force $\vec{F}$ is the time derivative (the change over time) of momentum $\vec{p}$".
This is somewhat related to Delta ($\Delta$). For linear functions, one can calculate the slope $s$ via "rise over run",
$$
s = \frac{\Delta y}{\Delta x}
$$
If your function is not linear, you can still approximate the slope for a short section with this. To get more accurate results, you can shorten your Delta. In the limit of $\Delta \to 0$, you get the differential mentioned in the Wiki article. Mathematically, the slope at point $x_0$ is then also called the derivative of $f$ at $x_0$
$$
s = f'(x_0) = \lim_{\Delta x \to 0} \frac{f(x_0+\Delta x) - f(x_0)}{\Delta x}
$$
So, the force $\vec{F}$ is the time derivative of your momentum $\vec{p}$,
$$
\vec{F}=\frac{d \vec{p}}{dt} = \frac{d}{dt} \vec{p}
$$
EDIT: so, what the answer to the question "what is the meaning of $d$?" should probably be is: if you make your $\Delta$ really, really small (infinitesimally small, to be precise), you get $d$.
