Imagine you are in a swimming pool and you start to spin around really fast. The water around you starts to move too and if a toy boat was in the water, it would start to move along with you. This is called "dargging" - the water is pulling the boat along with it.
Now, let's think about space. It's not made of water, but it's still a "medium" that can be dragged around by really heavy objects like planets or stars. This is called "frame-dragging".
Let's think of space like a big blanket. If you put a heavy ball on the blanket it will make a dent, or a "gravity well." If you put a spinning top on the blanket next to the ball, it would spin around and the blanket around the ball would move with that spinning top. This is what happens to space near a spinning object- it twists and rotates around the object just like a blanket would.
This effect was first predicted by Einstein's theory of General Relativity which showed that objects with mass create a curvature in space-time. This curvature is like a dent in the blanket, and when an object is spinning (like a planet or a star), it drags space around with it.
So, to sum it up - frame-dragging is a phenomenon that occurs when really heavy objects spin, which causes space-time to twist and rotate around the object, acting somewhat like a giant vortex in space.