Compression Socks

Some people like them and believe they benefit their performance and/or recovery.  The science is spotty on either of those.  In general, most research appears to downplay potential for performance benefits (although some argue they could make you more aero) and is a bit more mixed on their potential as recovery aids.  You see them mostly because they are 'trendy' and the marketing for the potential benefits has been stronger than the science.

Pretty much what JK said.  The only things I'll add are that even if they do aid in recovery, there is some evidence that recovery aids may actually impair fitness adaptations, because inflammation is part of the body's repair process.  Reducing inflammation prematurely may reduce fitness gains associated with those repairs.  This is an area of research that we will likely see more of in the next few years.

One time that consensus says they are useful is during multi-hour car rides or flights after long hard races.  Wearing them then can reduce the odds of deep vein thrombosis (DVT).