When you rededicate, you commit yourself to some project or idea once again. After years of not studying Spanish, you could decide to rededicate yourself to becoming truly fluent before your trip to Barcelona.
You can rededicate your life to doing good works — in other words, devote yourself to charity again after taking some time off. Your friend who had given up on her yoga practice after pulling a muscle might decide to rededicate herself to doing yoga every day and finally being able to stand on her head. When you dedicate, you devote — add the "again" prefix re- and you do it again.