In the past, around the Industrial Age and Columbian Exchange, people typically moved because of settler colonies, labor systems such as indentured servitude, natural disasters such as the Irish Famine, for GGG in the Columbian Exchange to the New World (God, Glory, Goods), and slavery as conducted by the Atlantic Slave Trade.
Today, I would argue most people migrate because of the harsh, political conditions of their place of origin. In Mexico, the government is corrupt and ruled by gangs, thus many people move to the US. Another example is the Yemen Civil War which occurred in 2015.