What factor accounted for immigration becoming a global phenomenon during the late nineteenth century?

I'd say there were factors on both sides of the Atlantic. 
Inthe United States, sudden and rapid industrialization during the Gilded Age created a
huge demand for labor at the same time as the Western territories were being secured and
cheap or free land became available.  This was an irresistible magnet to people on in
Europe and Asia as they sought to escape poverty and chaos in their own
nations.

In Europe, economic issues and political upheaval,
especially in Germany and France during that time, led to large numbers of germans,
Poles, Russians, Jews and Italians immigrating in the same 30 year time
span.