The flexibility in certain parts of a plant, such as leaves and stems, is due to the abundance of collenchyma cells. Collenchyma cells are one of the three types of ground tissue in plants and are responsible for providing support and flexibility to growing parts of the plant.

Option 1, parenchyma cells, are another type of ground tissue in plants but they are not specifically responsible for providing flexibility. They have a variety of functions including storage, photosynthesis, and gas exchange.

Option 3, sclerenchyma cells, are the third type of ground tissue and are responsible for providing strength and rigidity to the plant. They have thickened, lignified secondary cell walls that make them less flexible compared to collenchyma cells.

Option 4, xylem and phloem, are vascular tissues responsible for transporting water, nutrients, and sugars throughout the plant. While they play important roles in the overall structure and function of the plant, they are not directly involved in providing flexibility to certain plant parts.

Therefore, the correct answer is option 2, collenchyma cells.