Nano, in the sense of units of measurement, is very small. In the metric system, the "nano" prefix means "one-billionth." You may have heard of certain computing tasks taking place in terms of nanoseconds-- these are very short bits of time indeed.
Nano in the Apple realm refers to a product that does much the same as another Apple product, but is much smaller in size. The current iPod nano does almost everything the iPod classic does, including video, but is considerably smaller and lighter.
The rumored iPhone nano would, thus, share much of the full-size iPhone's functionality-- albeit with a smaller size, smaller screen (9 apps on the home screen, perhaps, instead of the iPhone's 16) and smaller data storage capacity.
You can go to the apple.com website to compare the iPod classic and iPod nano, and extrapolate the possibility of an iPhone nano from there.
I figured you could use a brief respite from the "shredding".