Stolon on strawberries

Hi Jack,
If a plant is large, it can make more flowers, and so more fruits, in the case of the strawberry the fruit is in the form of tiny achenes, seeds on the swollen red receptacle (actually the base of the flower, and part of the parent plant).  The strawberry that we think of as a 'fruit' is a clever way that evolution has found for the strawberry plant to disperse its seeds.  Animals eat the nice red bit, and then deposit the seeds away from the parent plant, as animals do, in a generous dollup of fertilizer, so that new generations of  the plant will grow.

So, returning to your question, the stolon allows the plant to send out 'runners' which terminate in 'another' plant, so each individual strawberry plant contributes to a 'larger plant' which can develop more flowers and seeds and increase the numbers of the next generation.  It's simply a way that this species of plant increases the number of potential new individuals in the next generation.  The individual plants that results from the stolon have normal gravitropic roots.

MAny other plants use similar methods of vegetative growth, eg brambles.