How does migration facilitate specialisation? When migrant workers arrive in a country, how do they facilitate specialisation? Is it by freeing up workers from jobs they do not want to do?
Workers may have different skills. If immigrant workers are good at farming then domestic workers can shift into non-farming activities.
Workers increase the total population and larger populations can sustain greater specialization. For example, with enough people we can have an artisanal pencil sharpener and professional crossword puzzle maker but a smaller population couldn't sustain that as a career. 
Migrants tastes may differ from domestics and domestics may develop businesses to address these tastes. For example, bidets are not common in the United States but Kohler, an American toilet manufacturer, is happy to have its workers make them for immigrants that enjoy them.