Some scientists think that nanobots could in future be used to make things, perhaps even to manufacture other nanorobot bodies. They could become self replicating, just like living creatures. It's not so far fetched - this small robot can already build copies of itself
Grey-goo and the end of the world!
If nanobots were to make other nanobots - reproducing as living things do, would this be a risk?. The grey-goo theory ask what might happen if such nanorobots ever started to reproduce out of control, and wonders if the resulting grey-goo of nanobots would end up consuming the whole of planet Earth.
But given that independent nano-robots haven't even been built yet, yet alone self replicating ones, is this a realistic fear?
All research carries a degree of risk, as it is looking at the unknown. The important thing is to assess the possible risks, to ask whether they are worth it. See Measuring Consequences for more on this.