To move forward or advance something; also to set a clock/watch ahead (make it show a later time).
時計を5分進めておいたほうがいい。
It's better to set the clock five minutes ahead.
列を詰めて前に進めてください。
Please close the gap in the line and move forward.
To carry forward plans or work; to proceed with or advance (projects, initiatives, tasks).
プロジェクトを順調に進めるために会議を開いた。
We held a meeting to keep the project moving smoothly.
新製品開発をさらに進める必要がある。
We need to further advance the new product development.
To raise or promote (someone or something); to develop or stimulate (e.g., appetite).
彼を部長に進めるつもりだ。
I intend to promote him to department manager.
辛い料理が食欲を進めることがある。
Spicy food can sometimes stimulate the appetite.