Many people would consider increased freedoms in and of themselves an element of social progress. On another level, one can argue that wealthier nations tend to measure high on both freedom and on social progress indicators, having lower levels of corruption, extreme poverty, infant mortality, and other social problems.
In general, in freer societies, people are more able to discuss and protest various forms of injustice, leading to politicians focusing more on those problems. In free, democratic societies, voters can also turf out politicians who impede social progress.
As women, for example, have increased amounts of freedom, they are more able to leave marriages in which they suffer spousal abuse or refuse genital mutilation. More oppressive countries which limit the freedoms of women have a greater incidence of abuse of women.
However, freedom and democracy are not a complete path to social progress as freedom can also mean, for example, freedom to impose upon a nation laws that discriminate against homosexuals.