Why is an object's vertical velocity increase the farther it moves away from you?

I am assuming you are referring to something like a ball
or stone that you throw in a straight line away from you?

The object is subject to the force of gravity which acts
towards the center of the earth or in the downward
vertical direction.
This force accelerates the object vertically downward.
An accelerating object is increasing its speed...until it
reaches the ground, then it stops accelerating and ignoring
any bounce its vertical velocity is then zero.

The best way to think of this is throwing something off a building or mountain.
As the object moves away from you gravity starts accelerating the object
and it can acquire a very large vertical velocity.