There are TWO types of headphones that do noise cancellation... active and passive. I have and use BOTH.
Is a cheap version of an active headset. The way these work is they sample the external audio and then play it back INSIDE the ear phones out of phase so the background sound is 'removed'. These are at the budget end but are surprisingly good for £30 and remove about 70-80% of the background noise.
Used with ear plugs if you want to sleep they block out 99% of all noise so an infant crying in an airline cabin (why on earth do people fly with a baby on holiday?) can cry until you land you don't hear a thing.
The passive headphones I use are in ear Genius noise cancelling headphones. They work by not letting the back ground noise into the ear canal.
There are much more expensive sets about but I didn't want to spend >£200+ on them.