Clusters of neutrons and protons can form in a very large nucleus. If a cluster of 2 neutrons and 2 protons forms the binding energy is large compared to other clusters and the alpha prticle formed gains kinetic energy equal to the binding energy. This energy is not sufficient to leave the nucleus.However, if you consider the wave properties of matter, the alpha particles position can be calculated from the probability that the alpha particle is in any one place. There is therefore a small, non-zero probability that the alpha-particle can be positioned outside the nucleus i.e. it can tunnel through the potential energy barrier without gaining any extra energy.