Atoms are formed by creating nuclei (cores) of one, two, three, four, or more positively charged protons, adding a roughly equivalent number of neutrons (neutral particles, with no charge), and then surrounding them with a cloud of negatively charged electrons. The protons and neutrons are roughly all the same weight, and form a tightly bound central structure. The electrons have negligible mass in comparison (imagine a fly buzzing around a cow), and are found in a diffuse cloud which can extend far beyond the nuclear region.
Each element (hydrogen, helium, lithium ...) contains a different number of protons. These positively charged protons attract negatively charged electrons (just as in films, opposites do attract!), binding them to the atomic nucleus with a force that scales with the number of protons, and so can be predicted for a given element.
When identifying which isotope of an element is under discussion, we precede the element shorthand name (H, He, Li, Be, B, C, N, O ...) with a superscript of the total number of nuclear particles (protons and neutrons) and follow it with a subscript of the atomic number (number of protons). You will quickly notice that for many elements, the number of neutrons is equal to the number of protons. The number of electrons is not defined in this label. When an atom has the same number of protons and electrons, we say that it is neutral, because the number of positive and negative charges balances exactly. If an atom gains or loses an electron, we say that it is ionized.
We can draw an analogy between the movements of the planets around the Sun, and the electrons which surround the atomic nucleus. In each case, the central source attracts the smaller objects, with a force which drops off with distance. The planets are held in place by the gravitational attraction of the Sun, while the negatively charged electrons are bound by the positively charged protons within the nucleus. In each case, it takes energy to move away from the central attractor.
There is a critical distinction between the two models, however. While a planet could be found at one A.U. from the Sun (the radius of the Earth's orbit), or 1.237 A.U., or any other similar distance, an electron can only exist at set energy levels. If you add a bit of energy to a planetary orbit, the planet will spiral slightly out away from the Sun. An electron, however, can only absorb photons with energy in quantized packets sufficient to shift it exactly to another energy level. If offered a photon with twice the necessary energy, half of the necessary energy, or 1.237 of the necessary energy, it will not change its state.