What do we mean when we say that a nucleus undergoes radioactive decay?

A nucleus undergoing radioactive decay means that this nucleus is relatively large and contains many neutrons leading to instability in the naturally occurring state.
Therefore, this large nucleus emits radiations in the form of alpha, gamma or beta particles. During this process, the nucleus is actually emitting a part of itself in order to reach a more stable element.

Example:
carbon-14 emits radiations and decays forming nitrogen.