An atom can be modeled by a proton-neutron core with a bunch of electrons "floating around".
Quantum mechanics gives us a way to describe the interaction between the core and the electrons, and to draw the conclusions that the atom can reach discrete "energy levels" E0, E1, E2, ..., En. The lowest level E0 corresponds to the fundamental state of the atom.
However, external excitation (thermal energy, interaction with photons,etc...) can help the atomic system to reach a higher energy level.
If an atom is in a given energy level E(n) at room temperature, and you promote it to a higher one (let's say E(n+1) ) by interacting with it, it will naturally want go back down to E(n). When doing so, it will release energy in the form of a photon.
We know from the planck relation e = hf that the wavelength of the photon is directly related to its energy. So the gap E(n+1) - E(n) determines the wavelength (color) of the emitted light.
The structure of energy levels (and thus the value of E(n+1)-E(n) ) can be predicted by quantum mechanics for simple atoms. The results of this prediction will be different for every atom (because the interactions to take into account differ according to the number of protons and electrons in the system, and thus lead to different equations).
so every atom will have its own "jump height" and color.
Of course, nature of matter is a very complex subject, and this is an oversimplified answer free of all mathematical considerations. I hope it is in adequation with what you expected.