The world we live in is full of shortcomings. To perfect it, we rush around all week long, working and exerting ourselves in a variety of ways. However, on Shabbat, which is like the World to Come, we are commanded to cease all work and act as if everything has already been perfected, with no further need to rush around. We are meant simply to delight in the holiness of Shabbat and take a faith-filled look at the perfect inner essence of the world as God created it. There is a mitzva to express this spiritual perspective by walking at a leisurely pace on Shabbat. Thus the Sages expound: “‘Not go in your own way’ – the way you walk on Shabbat should not be like the way you walk on weekdays” (Shabbat 113a).
Therefore, running is prohibited on Shabbat, as is striding. This prohibition applies to one who is going somewhere for his own sake, in which case he should walk at a leisurely pace to honor Shabbat. However, if one is going to attend a Torah class or to pray, it is a mitzva for him to run (Berakhot 6b; SA 301:1), because running for the sake of a mitzva does not detract from the honor due Shabbat. On the contrary, it expresses the spirit of Shabbat, which allows us to rest from the troubles of this world. This peacefulness in turn encourages us to serve God.
One may run and jump if one benefits greatly from it. For example, one may run in order to get out of the rain, and one may jump over a puddle to avoid dirtying his shoes. One may also run in order to watch something enjoyable (Shabbat 113b; SA 301:2-3). Children and teens who enjoy running may participate in games that involve running, since this type of running is pleasurable rather than burdensome (SA 301:2). Also, adults may jump for pleasure as part of playing with small children.