1. To advance forward while simultaneously causing someone or something to advance forward as well. The player moved forward with the ball and kicked it toward the net. The man moved forward with his three children through the crowd.

2. To begin undertaking, developing, or making progress in some activity or project as planned. We've had some setbacks, but it's important that we keep moving forward with our original idea. We can move forward with construction as soon as we have the necessary permits.