1. to advance; to move forward; to put (a clock, watch) forward
僕らはひとまず校舎の方へと足を進めた。For now, we headed toward the school building.
2. to carry forward (plans, work, etc.); to proceed with; to make progress in; to further; to advance; to hasten; to speed up
これでようやく話が進められるわ。Now we can finally move the conversation forward.
3. to raise; to elevate; to promote; to develop; to stimulate (e.g. one's appetite)