Historically the Wild Geese were Irish Mercenary soldiers fighting with French Army in the period after the Treaty of Limerick (1691).
As part of the Treaty Patrick Sarsfield lead the remains of the defeated Jacobite army in Ireland into exile in France. These men were to make up the Irish Brigade of Royal French Army. In the following years volunteers to the Brigade would take ship from Ireland (under British rule, who were naturally opposed to subjects joining forgien armies) and recorded on the manifest as Wild Geese. Hence the name.
The term has come to refer to all Irishmen fighting with the continental armies and those in the American Civil War. Irish units could be found in the armies of Spain (regiments of which went far to the Flight of the Earls), Russia, Poland, Austria and the various Germanic Kingdoms.