A standard deviation is a measure of how unusual a set of data is if a hypothesis is true. Physicists express standard deviations in units called sigma, σ. The higher the number of sigma, the more incompatible the data are with the hypothesis.

If the data are incompatible enough with a hypothesis that says the experiment will find only background, that could constitute a discovery. Typically, the more unexpected or important a discovery, the greater the number of sigma physicists will require to be fully convinced. Five sigma significance is traditionally required to claim a discovery of a new particle; this was the threshold passed by the Higgs boson when its discovery was announced on 4 July 2012.

Check out the Statistical Significance cheat sheet to learn more.