Just as 3-D printers create objects that have three-dimensional characteristics, 4-D printers create objects that have four-dimensional characteristics, in that they include a dynamic component that causes their structure to change over time -- relying on water, heat, or light to activate them.
Using a multi-material printer, it's possible to generate objects with these properties all in one go. Such "programmable materials" may one day mean that you can buy flat-pack furniture at Ikea, take it home, spray it with a garden hose and then watch it assemble itself. We don't even have to speculate: MIT is working on this exact thing.
To understand how a programmable material works, think about what often happens to a thin strip of wood if you get it wet: It warps, as different parts of the wood swell in slightly different ways. Usually, this is bad, because the warping is unpredictable and related to the type of wood, the patterns in the grain of that wood, how and where it gets wet, and so forth. If you could somehow predict the warping, though, you might be able to find a piece of wood that you could deliberately warp into a shape that you wanted, just by adding water.
This is not a thing that we can do with natural wood, but that's fine, because we don't need natural wood anymore. With 3-D printing, it's possible to manufacture pieces of wood with whatever composition, thickness and grain characteristics that you wan.
With a comprehensive understanding of how the material behaves, along with computer models, you can 3-D print a piece of artificial wood that's been "pre-programmed" -- using carefully constructed layers of various thicknesses and grain directions -- to warp itself from flat into exactly the shape you want. Just add water.