The factors that may come from one side more than the other may include light, gravity, touch, even water. If it light is the uni-directional stimuli the tropism that is caused is referred to as phototropism. If the factor is gravity then the plants have a gravitropic response. If one side of a stem is touched more than another then the plant will grow towards the touch. This causes tendrils to to grow around fences or other stems.
Plant roots can only grow in moist soil so root tends to follow the water gradient.
Phototropism When light is received by a plant in a uniformly distributed manner the plant grow up straight. If more light comes from one side of the plant than another, the plant will grow toward the brighter light source provided that the light source contains blue wavelengths. Auxin affects the stem growth in length through a process known as acid-growth. Cells with elastic cell walls stretch out more than cells with less elastic cell walls. With uneven distribution of IAA in plants placed in uni-directional light the side with the most light has less IAA and therefore has less elastic cell walls than the cells on darker side of the stem which are more elastic and are stretched out longer than cells on stem on the side more light.