What is 1,3-Dipolar cycloadditions?

A 1,3-dipole is a three-atom $\pi$ system with four electrons, written with formal charges at its ends or in the middle, such as an azide $\ce{R-N=N+=N-}$, a nitrile oxide or an ozone molecule. A 1,3-dipolar cycloaddition is its [3+2] cycloaddition, a six-electron reaction, with an alkene or alkyne, giving a five-membered ring.