Radioactive decay, or radioactivity, is basically a process in which an unstable nucleus loses energy by the emission of radiation in the form of a particle.
This is more of a physics concept than a basic chemistry concept, but it is very relevant for chemists.
Not all atoms that exist are stable, some are what you could call “not meant to be”. Most of the matter that we see is made up of combinations of protons, neutrons that are stable (stable atoms, specifically, stable nuclei). But other combinations of neutrons and protons give rise to unstable nuclei, that eventually fall apart. This is the basis of radioactivity in simple terms.
During the decomposition of these unstable atoms, energy is released in the form of particles. This release of energy can be detected, and it is what we call radiation. When this process takes place, a new nucleus is formed, and therefore, a new atom. This new atom can be also unstable and keep releasing radiation until it turns into an stable atom, which no longer emits energy as radiation.