Plants are living things and plants do move.
The opening and closing of flowers, the dropping of leaves at the end of the day.
The change in direction of the stems, leaves etc towards the light.
The movement of roots towards the areas which have better water and nutrition
The spontaneous bursting of pods of some plants to disperse the seeds
All these are movements related to the plants. Of course, they cannot move like man, animals and birds but they do exhibit movement in their own way.
For instance, the simple experiments we used to do in school days, placing a plant in a dark box with only one hole or window for light. After a few days, the plant (leaves etc) would face and start growing towards the light source.
Moving further, we should recollect the experiments of Professor Jagadish Chandra Bose. He invented the 'CRESOGRAPH' an oscillating recorder. He recorded that plants move very small fractions of an inch. He also put forth that plants experience pain and pleasure.(https://www.thebetterindia.com/76587/jagdish-chandra-bose-indian-biophysicist-radio-plant-physiology/).
Recently there are some articles which suggest that plants are just like us and animals, they have sense like us. It is just too slow and perhaps we should change our perception by not comparing the free movement that is seen by humans to that of plants.(http://www.bbc.com/earth/story/20170109-plants-can-see-hear-and-smell-and-respond).