Plaster is a kind of soft, thick, sticky goop, usually made out of sand, lime, and water. We spread plaster onto walls. It goes on smooth and flat, and when it dries, it's hard and strong.
When you've plastered a wall, you've given it a strong, smooth surface that will last for a long time. Maybe not forever, though: you might have to scrape off the old plaster sometime and start over.
So, just like we plaster a wall by covering it completely with a flat, sticky substance, we can plaster other things onto other places. To plaster something with things is to cover all of it (or almost all of it) with things in a way that seems flat, strong, sticky, or permanent.
People have plastered flyers all over this board. That is, they've totally covered this board with lots of flyers.
Racecars tend to be plastered with logos. This racecar is plastered with the Shell logo, the Pennzoil logo, and the AAA logo. Almost the entire car is plastered with logos!
If you get wet—because you got sweaty, or you got rained on, or maybe you fell out of your boat—then your wet hair may be plastered to your face, and your wet clothes may be plastered to your body. That is, they're sticking to you, wet and flat.