To answer this question, it is probably easiest to first define what viscosity is.
Viscosity is a trait or measure of a liquid that has resistance to "deformation" or movement when put under stress, whether that's gravity or some other force.
Example
Water has a very low viscosity because it flows easily and freely. It is relatively frictionless when compared to a liquid like honey or molasses, which are both extremely viscous.
So if you were to flip a cup of water upside down, the water would spill everywhere immediately.
If you were to flip a cup of honey upside down, you might be there a while before it fully leaves the cup.
So, What Is Dynamic Viscocity?
Now that we know what viscosity is, let's move on to dynamic viscosity.
Definition
It is defined as, "the force needed by a fluid to overcome its own internal molecular friction so that the fluid will flow."
Specifically, it's a measure of liquid's resistance to move across a horizontal plane.
Example
To illustrate this, imagine pouring a cup of water over a metal baking sheet.
Water, since it has a low viscosity, it will likely spread out all across the baking sheet. Its internal friction is just too low to keep its own shape (unless it's frozen).
Now imagine dripping honey on the sheet. It will mostly retain the shape it was in when it came in contact with the shape.
Now, if you came back to that baking sheet later, the honey might have spread out across the baking sheet.
But that difference between water and honey, and the time it took to move across that plane is dynamic viscosity.
Dynamic viscocity is not to be confused with kinematic viscocity.
Summary
Dynamic viscocity is a measure of liquid's internal molecular resistance to move across a horizontal plane.