It means "during the last 10 years." E.g. Over the past ten years the UK has seen an increase in the number of migrant workers. - During the time period from 2004 - 2014 the number of migrant workers in the UK has increased.

Events that have taken place in the last ten years, so between 2004 and 2014 "Over the last 10 years I have become better at studying for exams" is an example or "The trees in the garden have grown bigger over the last 10 years!" something like that :)