For each proton there is one electron. The electrons orbit the nucleus in "shells". The "shells" consist of "subshells".
If an electron is hit by a photon--the thing that carries the energy, and which we perceive as light or heat or some other length of radiation--the electron absorbs the photon.
With more energy, the electron moves further out from the nucleus. At some point the electron gives off a photon--losing energy--and drops back to a lower subshell or shell.
Photons travel in waves--like the sine waves from high school math. The distance from zero to maximum to zero to minimum back to zero is called a wavelength.
Every color has its own wavelength. Not just "red, orange, yellow", but each different shade of yellow, etc., is a different wavelength.
Electrons traveling around a nucleus have their own wavelengths. They can only use a path of 1, 2, 3, etc., wavelengths--not 1.5 or 2.7, etc. So when an electron jumps to a higher shell, it would go from a path of 3 wavelengths to 4, then back to 3 at some point.
They also can only absorb and emit photons that have the same wavelengths.
Because electron paths can't cross, etc., each element has a set of paths unique to that element. The combination of paths for platinum means that the light it can absorb and emit looks silver to us. Gold has a different combination of paths, and the light wavelengths it can absorb and emit look yellow to us.