One of the oldest recognized and most often studied properties of plant growth, phototropism is the slow growth
of a plant towards a light source
This growth is a hormone mediated response. At the tip of a growing plant, the apical meristem tissue synthesizes the plant hormone auxin -- and auxin synthesis is reduced in the presence of direct light*. Thus, on the shady side of the root tip ( e.g. the side away from the sun) the auxin production is highest; the hormone is transported down the root tip into the cells of the stem, where it promotes cell growth in the direction of the stem axis.
In this way, the shady side of the plant is induced to grow and elongate faster than the lighted side, pushing the stem away from the shady side -- i.e. towards the light source.
An astute m_turner points out that the most well known example of this phenomena is found in, aptly enough, the sun flower
*FYI: The synthetic pathway and photoregulatory mechanism of auxin are not fully known. The structure strongly resembles the amino acid tryptophan, and recent work has suggested that the synthetic enzyme may use a biochemical relative of tryptophan as its substrate -- though it is possible for the plant to synthesize auxin in the absence of this amino acid. The light-depended synthesis is probably mediated through any one of several plant photopigments, most probably a pigment sensitive to blueish light.