Rashbam and others take this as a command not to delay the fulfilment of a vow or oath. If you promise something to the Almighty you should carry it out promptly.
This interpretation has a great deal to commend it. It recalls the recommendation, “When a mitzvah comes into your hand, don’t let it get stale” (Mechilta, Parashat Bo).
A particular example which is part of daily living has to do with saying one’s prayers. When it is time to daven one should not find every possible excuse to delay and to keep God waiting.
There is another way of understanding Moses’ warning. “Whatever comes out of one’s mouth he shall do” can also be telling a leader to listen to his own words and heed his own message.
The Mishnah lays down something similar in the laws of saying the Shema: “He who says the Shema but does not make it audible to his ears has not carried out his duty” (Ber. 2:3).
There is a rabbinic saying that a person who speaks well but does not take his own advice is like someone who does the washing but remains unwashed himself (Tosefta Yevamot 8:4).
Unfortunately it sometimes happens that a leader, even a rabbi, is a genius at preaching values and ideals but is no role model. No wonder his audience says, “Why should we listen to you? You are no better than we are!”