Take a brief look around you. Everything you see is made from atoms, those incredibly, intangibly tiny things, the building blocks of stuff. If you can see it, it's made from atoms.
So what are atoms made of? Scientists only answered that question a few decades ago indeed, they only came up with the modern idea of the atom as we see it now just over half a century or so ago. Atoms, as we know them today, are made up of three crucial components neutrons, protons and electrons. The neutrons and protons sit together in the middle of the atom, called the nucleus. The nucleus is incredibly dense and contains most of an atoms mass.
The electrons, however, are not in the nucleus. Rather, they fly around outside it in various orbits, at differing levels from the atom. The actual position of an electron, according to quantum mechanics, is impossible to pin down, so we have to settle for them being a certain distance from the atoms and travelling at a certain speed.
The fact that electrons are not in the nucleus of the atom means that they can be taken off it. The nucleus is incredibly dense and powerfully charged, and so splitting it requires masses of energy. Nuclear fission is just that splitting the nuclei of atoms.
To remove electrons from atoms is far far easier. We do it every day, all the time, mostly without noticing. When you turn on a fluorescent light for example, electrons are removed from their atoms. Static electricity, and indeed all electricity, relies on electrons that are not attached to atoms.
Once you remove an electron from an atom, you get an ion. The definition of an ion, something I seem to have been working up to for quite a time, is simply that it is a 'charged atom'. To understand this requires an understanding of electrical charges inside atoms. Protons are positively charged, and we say they have a charge of +1. Electrons carry a negative charge, -1, and neutrons carry no charge, as their name suggests. In a normal atom, the number of protons is equal to the number of electrons. That means that the overall charge of the atom is 0. However, if the atom was to lose an electron, then it would become positively charged. Atoms can also gain electrons, which means they become negatively charged.
Take an atom of oxygen as an example. Oxygen usually has 8 protons and 8 electrons. However, if the oxygen was to gain 2 electrons, then it would have 8 protons and 10 electrons. That means that it would gain a charge of -2. If this atom of oxygen was to then lose 3 electrons, its electrical charge would become +1, as we now have one less electron than proton.