High intergenerational mobility means a high positive relationship between parent's income and adult children's income.
The greater the intergenerational mobility the less the next generation's income depends on opportunities than on predetermined factors... factors related directly to parent's income levels..
What studies, both empirical and theoretic, show is that in some countries the greater the father's income the greater the adult male childrens' income also is, while in other countries there is little relationship. It also shows that for those born into families with low income the probability that the adult children will remain as low income adults is also higher. The reasons are varied but have most to do with early childhood education and parental support which is highly related to income level of the parent.
Here is an article which contains a couple of links to very enlightening studies on the subject. One of these links is a study shown in presentation form: shows method of determining intergenerational mobility, and several charts showing the relationships over several western countries --- US, Canada, western european countries, including Scandinavian. Results are remarkably different showing US and UK are the countries with the least intergenerational mobility, the scandinavian countries with the most. Remarkably different! There's also a chart relating intergenerational mobility to cost level of education, where the US is so far off the normal relationship of one to the other that it begs the imagination.... one could almost literally say "off the charts"... in the negative sense. .
All for your continued enlightenment --- enlightenment is just one way to keep propoganda from taking you hostage.
If you think about equal opportunity of success, this information will provide some insight to why equal opportunity is not so much in fact and in the US equal opportunity is actually the least. Gee... I wonder why that could possibly be? Anybody proposing "leveling the playing field" to provide equal opportunities needs to understand means of doing so. Anybody believing the US is the global leader in opporunities needs to see the facts on "equal opportunity"... the US is the least equal opporunity nation of those studied in the western world.