High Pockets is a common nickname given to tall people. The first recorded usage I've found is from around 1915 where the nickname was given to baseball player George Kelly.
High Pockets was also a silent movie made in 1919. The main character is "High Pockets" Henderson.
High Pockets is also used to make fun of people that wear fancy trousers -- which makes it related to the term fancy pants. Used in this fashion it has a connation that the person is unduly concerned with social status.
I suspect that the usage of this term has faded over the years. I still hear it occasionally in the rural areas of Missouri and Kansas, but hardly ever mentioned on TV, radio, or in urban areas. You'll still find a number of championship horses, cows, dogs, and cats with this nickname and there's even a prototype hovercraft named High Pockets.