What is a pocket full of posies?

Posies are flowers

"Pocket full of posies" is a line form a nursery rhyme.

Lepers (those who had contracted leprosy and perhaps other sick people) during the middle ages in parts of Europe were forced to have flowers visible on their person (outside their clothes) so that others could avoid them.

The children of those times would often taunt the lepers by dancing in a ring around the sick and pushing them to the ground ("All fall down") or throw themselves to the ground imitating writhing in painful death throes.