In a very simple answer I'll take the Hydrogen atom, this has one proton in the nucleus and one electron orbiting it. Now if the atom absorbs energy and becomes excited the electron might move up in energy. If you do this with enough initial energy or in enough steps the electron escapes. Now if you leave the atom alone the electron will want to go back to the lowest energy state it can and will so lose energy by emitting a photon of a characteristic energy (depending on how much energy the electron loses). For each atom the amount of energy lost as the electrons lose energy is generally around a certain energy value that is different for each element (the electrons like to go down a certain amount more than others) so that they show spikes in spectra where these extra photons have been added to the spectra. This is a somewhat simplified view I should add, but it 's acceptable for an introduction.

An element's emission spectrum is the relative intensity of electromagnetic radiation of each frequency it emits when it is heated (or more generally when it is excited). When the electrons in the element are excited, they jump to higher energy levels. As the electrons fall back down, and leave the excited state, energy is re-emitted, the wavelength of which refers to the discrete lines of the emission spectrum. Note however that the emission extends over a range of frequencies, an effect called spectral line broadening. The emission spectrum can be used to determine the composition of a material, since it is different for each element of the periodic table. One example is identifying the composition of stars by analysing the received light. An absorption spectrum occurs when light passes through a cold, dilute gas and atoms in the gas absorb at characteristic frequencies; since the re-emitted light is unlikely to be emitted in the same direction as the absorbed photon, this gives rise to dark lines (absence of light) in the spectrum. The light emitted from an excited atom can not be directed toward the observer, so the light appears to be missing from the continuous spectrum. http://en.wikipedia.org/wiki/Emission_spectrum