When you have a dashboard with filters, select the filters and then on click View Report from the dashboard component. The report opens and is filtered in the same way as the dashboard, so you can keep analyzing data without missing a beat!
Filters conveyed from a dashboard to a report are called Linked Filters. You can remove Linked Filters from the report, but you can't edit them directly. Linked Filters don't persist after you leave the report. Consider the following screenshot: