The word tunneling (also spelled tunnelling) has more than one meaning.
The literal meaning is the digging of tunnels.
One of the most popular applications is in electron-tunneling microscopes (see scanning tunneling microscope) that are used to see objects that are too small to see using conventional microscopes. Electron tunneling microscopes overcome the limiting effects conventional microscopes (optical aberrations, wavelength limitations) by scanning the surface of an object with tunneling electrons.
See also Quantum Mechanics.