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An organism is an individual living system, made of one biological cell or an integrated assembly of biological cells. An Escherichia coli cell is an entire organism; a neuron is normally a specialized part of an animal. Metabolism, regulated exchange through cell membranes, and inherited information connect these very different scales. See OpenStax Biology 2e, 1.2: living systems and levels of organization.
Keep two questions separate: how many biological cells make the organism, and how those biological cells are organized. A yeast and an Escherichia coli are both unicellular organisms, but the yeast is a eukaryote and the Escherichia coli a prokaryote. A plant and an animal are multicellular organisms with eukaryotic cellular organization. Neither distinction ranks organisms as better or worse: natural selection acts on reproduction in particular environments.