The plant originated in South and Central America but is now found worldwide (at least anywhere the conditions for its growth are right) and has become something of a pantropical weed. The leaves close at night, but also under other stimuli, which is what makes the plant both fascinating and unusual.
When force (a simple touch in this case) is applied to the leaves of the plant the cells around this region lose turgor pressure (the force applied by water against the cell wall). This is due to a release of chemicals, including potassium, which drives the water out of the cells. Once the cell is without water it collapses. What we see is the leaves collapsing downwards.
No one knows for sure why the Touch-Me-Not (and other related plants) evolved this particular trait. Some scientists think that it has evolved to surprise animals. A leaf eater might think the plant was an insect after seeing the leaves bend so quickly away from its mouth and look for food elsewere.
Whatever causes the collapse, the Touch-Me-Not remains a captivating example of nature in (literal) action.
Top Image Credit Flickr User Whologwhy