Another name for the electron cloud theory is the quantum mechanical model. Both names refer to the idea that the locations of electrons circling a nucleus can only be approximated.
Erwin Schrodinger developed this model and used mathematics to claim that it is impossible to know for certain where an electron is at any given time. Electron movement around the nucleus takes on the appearance of a cloud, and wherever the cloud is densest is where there is the highest probability of finding an electron. Where the cloud is least dense is where the lowest probability lies. This theory usurps the previous notion that electrons have defined orbits and replaces it with the concept that they have different energy levels that help to approximate each electron's position in the cloud.