As I put on my trekking-socks last weekend, I wondered what might be the differences between the left and the right sock (besides the "mirrored" design)?
Well, basically the difference is just that their design is mirrored. However, I have the feeling that your real question behind the actual one is "Why do they have to be mirrored?"
Compared to "normal" socks, which are basically just a symmetrically knitted tube that is closed at one end and has a kink somewhere in the middle and can be worn on either left or right foot, more specialized socks such as trekking or running socks feature a more sophisticated design. This can include patches of stronger padding at spots of higher load or friction, areas where the fabric should only stretch into a certain direction, an asymmetric toe box, and similar stuff that are thought to make them as comfortable as possible, prevent blisters and/or help with the wearer's performance.* Typical patterns are things like a more padded heel and toe area (these could be also symmetric) and also more padding of the sole along the outside edge of the foot but less under the arch of the foot – and here the trouble begins, since our feet are not symmetric in themselves but are mirrored towards each other.
Hence, once you want to design socks (and also shoes and gloves where this is much more obvious) that take into account this asymmetry, you have to design pairs with an explicit right and left item.
*Some of those measures may be not of relevance for you or just some kind of voodoo that has no real justification but gives you a good feel and the manufacturer a higher price, but that's not the point here.
The right one goes on the right foot, the left one goes on the left foot. :P
But seriously, there should be no difference at all apart from the
mirrored design. After all you don't want your left foot, for example, to be padded more strongly or lightly than your right foot. Or for your right heel to have more/less grip than your left heel...