No doubt your child is starting a brilliant scientific career with this question!
"Boogers" are made of mucus. Mucus is made by mucus membranes. Your body has mucus membranes in all sorts of places: The stomach, intestines, nose, lungs, eyes, mouth, and the urinary tract all contain mucus membranes that secrete mucus.
Mucus contains mostly water and mucin (during a sinus or lung infection, it also contains dead white blood cells that have been working on the infection -- see How Your Immune System Works for details). It is the mucin that makes it sticky.
Mucin is a branched polysaccharide. If you have read How Food Works, then you know about saccharides -- they are sugar chains. Starch, for example, is a polysaccharide. As you've probably noticed, if you mix corn starch or flour with water, you get a sticky substance. Mucin is doing the same thing. Mucus is essentially a thin paste made of mucin and water.
Show your four-year-old how corn starch and water is sticky (especially as it dries out) and he will be looking at synthetic boogers!
For more information, see the links below.