The leaf was rinsed in water to rehydrate it. Iodine solution is an aqueous solution of iodine/potassium iodine - potassium tri-iodide; water is needed inside the leaf to enable penetration by diffusion.
Why the burette and the pipette are each rinsed with distilled water and finally rinsed with some of the solution that will be measured or transferred?
These are conditions necessary to avoid contamination or any other modification of the reagents.