We can safely say, that you are talking about electric current. It is defined as the "electric charge, which flows trough some point or region in given amount of time" (by Wikipedia):
$$
\textbf{I}=\frac{de}{dt}\hat{a}
$$
Bear in mind, that differential $d$ mrans small change, eg. small amount of charge divided by time needed for it to pass (which is also small). For understanding you can write as $I=\frac{e}{t}\hat{a}$. $\hat{a}$ is unit vector. This is an arrow according to which you determine direction, and number line. Let's say, that it points towards positive numbers.
We can express current as with upper equation. We divide the amount of charge which was moved in the direction into which $\hat{a}$ points in time needed for this. This equation and explanation is valid even if you don't know anything about electrons in material.
So in metals (or other conductors, where main carriers of charge are electrons) the change of charge $de$ is negative. When their velocity points in the direction of $\hat{a}$ (eg. is positive), the direction of current $\textbf{I}$ is negative, because of negative $de$. So you can se, that you have positive direction of travel for electrons, and negative direction of charge, which means, that they are exactly opposite. You could also say, that direction of velocity is negative, and current will than become positive, which will also lead us to opposite direction.