Migration is a touchy subject in today's world. To be honest, it was always a touchy subject, but Victoria 3 was never one to shy away from realism, just because of that, and, perhaps, in spite of that.
Mass Migration, as the devs explain, is a mechanic introduced to try and model the migration of large amounts of people to places such as the US, Brazil, and Australia in the 19th century. Mass Migration can happen when a particular culture experiences Turmoil, which is a product of having a large number of radicalized pops.
A culture that has enough Turmoil to meet the threshold has a chance to create a Migration Target somewhere in the world, which is a flag set on a particular State that attracts huge numbers of migrants from that culture over the course of a limited timespan to that State and any States neighboring it.
Migration Targets are more likely to be created if the Pops in the culture have a low Standard of Living and high Literacy, and particularly likely to be created if there is widespread starvation among the Pops of that culture.
The selection of States for Migration Targets is based on a number of factors, including the state’s Migration Attraction, whether or not the culture is legally discriminated against in the country, and if there is a logical ‘path’ that Pops of the migrating culture would be able to follow from their Homelands to the target, such as trade routes.
There is no inherent advantage in certain country ‘tags’ for who gets migrants, for example, the US tends to get migrations because of the availability of jobs and land combined with liberal citizenship laws, not because they have a built-in migration attraction bonus.
Another variable that can be added is the Migration Policy. This is a group of Laws that lets you set the stance of your country on migration. For example, whether you want to promote the movement of people from your core lands to your colonies, attract skilled workers from other countries for your manufacturing economy, or even just minimize all migration, both external and internal, as a way of maintaining your iron grip over the population.