| Terminal, meaning of an end, or boundary, is the key word in the phrase terminal velocity.
More specifically, in Newtonian physics, the maximum velocity a moving body can reach; approaching which acceleration linearly decreases1. This limit is brought upon by friction (a force opposing the motion), and is most commonly used when refering to free falling objects, in the Earth's atmosphere. There is a point where the velocity reached by acceleration is canceled out by air resistance and therefore remains constant for the remainder of the fall.
Let's define a few variables:
d = distance (m)
t = time (s)
v = velocity (m/s)
a = acceleration = v/t (m/s2)
m = mass (g)
F = force = m·a (N)
Now, let's concider, using basic algebra:
F = ma = mv/t
Force is equal to mass times acceleration, since acceleration is velocity over time, then it can be expressed as mass times velocity over time.
In order to comprehend this, we'll make a model of a falling object, where h means height, and is equal to d; meaning it is a distance. And where g is gravity (9.81 m/s2); an acceleration. These two tweaks are done merely for the sake of notation. Also, let's concider this one-dimentional motion, where up is positive:
F = -mg
The negative (-) is appended to g since it acts downwards.
Now let's come up with an opposing force— air resistance— which is a type of friction, f. A friction is a type of force:
f = ma
There's a little problem, however: Where does this new mass and acceleration come from? These are the properties of the millions of air particles the body hits while falling. Since these cannot be accurately measured, we will resort to appending a new value to the air resistance
f = b·v
Where b is an arbitrary constant of friction that varies depending on the density of the air, etc. Furthermore, if the resistive force grows as velocity increases, then we can set v directly proportional to f.2
Put them together:
Fnet = -mg + bv
The bv is positive as it acts upwards (against the downward motion).
When the terminal velocity kicks in is when the resistive force is equal to the force of the falling object, therefore making Fnet = 0. Therefore:
mg = bvterm
vterm = mg/b
Notice that if g (gravity) and b (air resistance coefficient) are constants, this would make m the independent variable and vterm the dependent variable; therefore the larger the mass, the larger the terminal velocity, and the more time the body will remain in freefall with an increasing velocity naturally caused by gravity.
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1 Since acceleration, i.e. by gravity, shows an exponential increase, the resisting acceleration of an opposing force will also grow exponentially, reverting the difference to linear.
2 If f is a force, it is measured in N, or g·m/s2. If f is equated to being b·v, it must still be measured in gm/s2: velocity is measured in m/s, therefore leaving g/s to be the units of b— The amount, in grams, of air, per second. | 
