1to push along (a bicycle etc while walking)
2to implement; to carry out; to introduce (a policy, system, reform etc)
3to promote; to advance (the practice of an art form, the use of a language etc)
Example
gōng sī公司cóng从xià gè yuè下个月kāi shǐ开始tuī xíng推行xīn新de的guǎn lǐ管理zhì dù制度。
公司从下个月开始推行新的管理制度。
The company is starting to implement the new management system from next month.