Caffè Lungo is a form of Italian coffee made in an espresso machine. It is essentially an espresso with about double the amount of usual water in it.
An espresso will have about 25 ml of water in it; a Caffè Lungo will have about 50 ml. It is less strong than espresso, but a bit more bitter, because extra water has come through the coffee getting extra compounds that would normally be left behind, and because of this, actually ends up with more caffeine than espresso.
At a bar espresso machine, you usually hold down the water pump handle from 15 to 30 seconds for a normal espresso. To change this into a Caffè Lungo, you will hold down the handle for up to 60 seconds.
The coffee will have a layer of "crèma" on top.
Some professional coffee tasters say that however accepted the practice of making Caffè Lungo is, it's plain wrong: that an espresso coffee basket filter is is designed to produce the right coffee taste only for 25ml of water being forced through it. If you want to add more hot water, they say, add plain hot water to preserve the taste balance.  Doing so makes the coffee a "caffè américano." Caffè américano is an espresso with fresh hot water added to it -- that is, hot water than hasn't been through the filter holding the coffee. It's the Italian attempt to provide North Americans with the kind of "large" cup of coffee that North Americans are used to with their drip coffee.
An even "longer" form of Caffè Lungo is Caffè Crema.
Frequently misspelt in English as "caffe longo."
Lungo means "long" in Italian.