Consider the following model of an atom:
Keep in mind that it is only a model and while it is a good model that elevates our understanding of the subatomic world, it is still just a model and reality will look different. How exactly? We don't know. The model is good enough, though, to understand what an excited atom is.
With this caveat out of the way, we can first try to understand what the ground state is. In the middle you have the protons and the neutrons which are densely packed to form the nucleus. It is positively charged by $Ze$, where $Z$ is the number of protons and $e$ is the unit charge. The same number $Z$ of electrons must orbit the nucleus to make this atom neutral. If we consider $Z = 1$, we have only one electron, and we can ignore rules, where exactly the electron is allowed to be due to the presence of other electrons (see Pauli Principle for further info).
The energy levels of the atom are quantized. That means there are only certain levels where the electron is allowed to orbit. In the picture they are shown by the gray circles ("shells"). If the electron sits on the innermost shell ($n=1$), it has the lowest energy. If it sits on the second shell ($n=2$), it has more energy, and so on. Typically, an atom wants to be in its ground state, where it has the lowest possible energy, i.e. where the electron is on the first shell. When the electron orbits on another shell than the first one, we call the atom excited. Exciting an atom can happen e.g. by irradiation, where the electron absorbs energy from a photon (light) to get to one of the outer shells. After a while, the electron will go back to the innermost shell, i.e. the atom returns to its ground state. Since it is in a lower energy state, energy conservation tells us, that it needs to emit the left over energy. This is done by emitting a photon, with a very typical wavelength (see spectral lines for further info). In the picture, this is shown by the red wavy line, where $\Delta E$ is the energy difference between the 2nd and the 3rd shell and also the energy the photon will carry away.