Neutrons play an important role in keeping the nucleus of an atom together. Without neutrons, protons would never stick together because the mutual repulsion of their positive electrostatic charges is too great. The only way to fight this repulsive force is to use an attractive force. Gravity is an attractive force but it is too weak at these low masses; however a "strong nuclear force" exists between nucleons (both neutrons and protons) that can overcome electrostatic repulsion at short range. Therefore, to make stable nuclei, nature sprinkles in a healthy dose of neutrons amongst the protons. The number of neutrons needed for stability depends on how big the nucleus is. For small nuclei the ratio of neutrons to protons is, perhaps as expected, around 50-50. As more protons are added, however, you need an even greater number of neutrons, until you get to an atom like uranium (the biggest naturally-occuring atom) which has 60% more neutrons than protons. The reason for this disparity is that the "strong nuclear force" drops off quicker with distance compared to electrostatic repulsion -- so protons on one side of a large nucleus need more and more neutrons around them if they're going to stick together. Now, as your question suggests, it is possible to have "too many" or "too few" neutrons as well. Nature lets you get away with this, but only temporarily. The resulting atom is unstable and will eventually balance its books by converting either the extra proton to a neutron, or vice-versa. When an atom does this it assumes a lower energy state and gives off a bit of excess energy at the same time. We call such an atom a "radioactive" atom. The energy it gives off is "radiation", and the probability of an atom making this transition at any particular time is related to its "half-life". To understand this, think of a bucket of identical radioactive atoms. The "half-life" is the time it takes for half of them to make the transition (also called "radioactive decay") to a lower energy state; or, put it another way, any radioactive atom has a 50/50 chance of decaying to a lower energy state within a period of time equal to its "half-life".