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I understand that the tangent vector is defined by the equation:

$$\lim_{h\to0} \frac{r(t+h) - r(t)}{h}$$

I know that the right and left hand limits are positive (even when $h < 0$, the negative denominator will produce a positive quotient). I know that this then means the tangent vector points in the positive direction.

What I don't understand is how the positive direction necessarily means the direction of increasing t? I guess I'm confused as how the positive or negative direction of the vector would correlate to increasing or decreasing values of t.

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    I suppose the curve is *parametrized* by $t$. Then increasing $t$ means "walking" along the curve and the derivative means the tiny vector when you take a really really tiny step along the curve. – 2017-02-27

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Think about it in terms of small finite differences:

If $h<0$, then $r(t+h)-r(t)$ points backward (the opposite direction as a particle moving along the curve). But then it's scaled by $\dfrac 1h$, which because it's negative flips the direction of it to the same direction as a particle moving along the curve.

If $h>0$, then $r(t+h)-r(t)$ points forward (the same direction as a particle moving along the curve). And then it's scaled by $\dfrac 1h$, but because $h$ is positive it doesn't change the direction.