This is the key understanding: energy (a particular line color) is released when an electron transitions from a higher to a lower energy level.
So 3 → 2 will produce one color, say red.
4 → 2 will produce another color, say green, and
5 → 2 will produce a third color, say blue.
Notice that ROYGBIV colors are listed from lower energy to higher energy.
Often times the energy levels are represented as a series of concentric circles surrounding the nucleus, lower energy being closer in and higher energy further away.
The most fundamental difference between the elements is the number of protons.
The more protons an element has, the closer in (the smaller) the energy levels get.
So and electron transition from 3 → 2 will produce one color in one element, but different color for a another element because the actual energy of the level is not the same.
You get a line spectrum because only some energy levels are possible. You get the color from a 3 → 2 transition, you get another color from a 4 → 2 transition, and all the in-between colors are missing because a 3.5 → 2 energy transition is not possible.
Here's a good site for representing the spectra of the elements.
Click emission, then click an element to see its visible spectrum.
http://jersey.uoregon.edu/vlab/elements/…