In radio terms, this option is allowing you to select between a 20MHz and 40MHz channel width. A 40MHz wide channel allows just a little more than twice the throughput (network bandwidth) of a 20MHz channel (because you get the equivalent of two 20MHz channels plus the "gutter" between them for one signal), but it takes up two channel slots.
In the narrow 2.4GHz band (originally used for b/g with 22MHz overlapping channels), only a single 40MHz channel will fit (note that 802.11n does not allow channels to overlap). This means that all 802.11n routers set to 2.4GHz (most of them) and to 40MHz channel width (fortunately not most of them) will be sharing the exact same radio space, and thus will slow eachother down. This can have an extreme impact in environments like apartment buildings and college dorms, where 802.11n set to 40MHz in the 2.4GHz band may perform worse (in terms of network throughput) than 802.11g.
This is the key reason that the WiFi alliance and, more slowly, manufacturers promote the 5GHz band for 802.11an. It is significantly wider than the 2.4GHz band, and allows for a comfortable number of non-overlapping 40MHz channels. The 5GHz band is also used solely by 802.11an (and limited other network applications), unlike the "general home RF" 2.4GHz band that WiFi shares with older DECT, analogue audio devices, etc (which are not WiFi aware and can significantly impact performance of nearby WiFi networks).
Even in the 5GHz space, though, there are only 2, 4, or 6 (depending on which U-NII bands your devices use, which is something I'm not familiar with) 40MHz channels available, so sticking to 20MHz is decidedly more neighbor-friendly in a crowded environment.