Stranded means the wire is actually made up of lots of other teeny little wires that are wrapped together to form a bundle inside the plastic sheathing. Very bendable, doesn't hold it's bend, and as long as you don't just continually bend this wire all over the place it will last a very long time, as in the little wires inside won't break, reducing your path for electricity.
The other type of wire is usually called "solid" and it's made up of just one solid piece of conductive metal. If you want to know what that looks like, just go to your closet and grab a wire hanger. That's solid wire. It's a LOT tougher to bend but it stays "in place" when you do bend it.