A colony-forming unit, CFU, is the cell or cells that reproduce on a petri dish that result in a visible colony.
When bacterial cells from a culture are placed on a petri dish in a medium with nutrients, oxygen, ambient temperature, etc., the goal is to grow the microscopic cells into colonies that can be seen. When these colonies are observed, one cannot assume that each arose from one cell. The colony may have arisen from a pair, a chain, a cluster, or a pair of cells that were so close in proximity they merged.
Here's an example: A test tube with 1 ml. of water containing bacteria is poured onto a petri dish medium. Imagine 1 bacterial cell landing alone; 3 cells landing in a cluster; and in another area 2 cells pair up. As the cells incubate and reproduce, we see 3 separate visible colonies. We cannot conclude that there were 3 cells per 1 ml of sample though. There were 3 CFUs per 1 ml sample. Additionally, some cells in the original sample may not have been viable. Viable CFUs can be counted in a sample, not viable cells.