Veins in a leaf
About 600 million years ago, the first plant cells evolved to be different from animal cells, and from earlier prokaryote cells, because they had a stiff cell wall made of molecules of carbon and oxygen, with some other elements like hydrogen, nitrogen, and calcium as well.
In plants, the part that corresponds to our bones and the part that corresponds to our blood vessels are the same thing: the vascular system. The earliest plants, and most plants still living on the Earth today, don't have any sort of vascular system, because they only have one cell and they don't need any support or food supply. Even some plants with many cells, like seaweed, don't need support because they float in the ocean. But some seaweed does have a way to transport water from one cell to another. The earliest land plants, like moss, also didn't have any support structure, though they do have some ways to transport water inside the plant.
But as plants moved away from the waterside about 300 million years ago and shifted most of their life cycle to the diploid stage, they needed to be able to suck water and food up from the ground and move them all through their stems and leaves, just as animals needed to move water and food through their blood vessels. They developed a branchind system of tubes like our blood vessels: the vascular system. Instead of a heart muscle that pushes the blood through our bodies, plants use transpiration, which is like our sweating. As water evaporates out of the pores in the leaves, the surface tension of the water pulls more water up from the roots of the plant. The plant hardly has to use any energy at all to keep its food and water moving.