Silence = closed back design. This is how many consumer-grade headphones are built anyway, but around here, you will often get recommended open back headphones--because they are regarded as better sounding for less money.
"Closed back" just means the outside of the earcup is solid, instead of having a grille or vent to let sound leak in and out.
A closed back headphone will naturally block out some noise. This is called noise isolation. To get the best isolation, you will need headphones that either:
1. Have large earcups which surround your ears entirely, with the cushions resting around your ears instead of on them.
2. Clamp hard enough to block external noise.
The idea behind both is to create a seal--less gaps between the ear cushion and your ears = less noise leaking in or out of your headphones.
Some headphones employ a different, or additional, means of achieving silence: noise cancellation. The most expensive Bose headphones do this, as do the most expensive Beats headphones, for example. The idea is that the headphones generate some additional sound waves to cancel out the noise coming in from around you; what this means to the consumer is that your headphones have additional circuitry, cost more, and will need batteries for the noise cancellation. Sound quality of noise cancelling headphones is generally frowned upon here.
