A secant line cuts a curve at two points. Take the points at $x = a$ and $x = a + h$, where $a$ is the x-value you care about and $h$ is the gap to the second point: the secant's slope is $m = \dfrac{f(a + h) - f(a)}{h}$, read aloud: m equals f of a plus h, minus f of a, all over h. It is the slope-of-a-line formula $m = \dfrac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the two points, with $x_1 = a$ and $x_2 = a + h$, so the run is $h$: rise over run, the average rate of change of $f$ between the two points. The tangent line touches the curve at $x = a$ alone and has the steepness of the curve right there. Nothing you can compute from two points gives it directly; what you can do is shrink the gap.

For $f(x) = x^3 - 3x$ at $a = 0$, $f(0) = 0$, so the secant slope is $\dfrac{h^3 - 3h}{h} = h^2 - 3$. Tabulate it as $h$ shrinks: $h = 1$ gives $-2$; $h = 0.5$ gives $-2.75$; $h = 0.1$ gives $-2.99$; $h = 0.01$ gives $-2.9999$. The slopes are closing in on $-3$, and $-3$ is the slope of the tangent at $x = 0$. Below, slide the point to $a = 0$, then drag the gap $h$ toward 0 and watch the secant slope close in on the tangent's. The read-out gives the tangent's slope at any $a$ as $3a^2 - 3$; the next lesson shows where that formula comes from.