As the electrons move from the higher energy level to the lower energy level, they release energy and ___________occurs. Energy is released only in...

"As the electrons move from the higher energy level to the lower energy level, they release energy and emission occurs. Energy is released only in specific quantum amounts. The available transitions for each element results in a signature line spectrum rather than a continuous spectrum."

This statement describes the behavior of the electrons in atoms when they gain energy. The increase in energy causes them to move from the ground state, which is closer to...

"As the electrons move from the higher energy level to the lower energy level, they release energy and emission occurs. Energy is released only in specific quantum amounts. The available transitions for each element results in a signature line spectrum rather than a continuous spectrum."

This statement describes the behavior of the electrons in atoms when they gain energy. The increase in energy causes them to move from the ground state, which is closer to the nucleus, to an excited state farther from the nucleus. Electrons are unstable in an excited state so they fall back closer to the nucleus releasing the energy they absorbed as light.

Because electrons can only occupy specific energy levels, there are only specific or "quantized" jumps that they can make. The light that is given off is only in specific wavelengths that correspond to these energy changes. When this light is observed as is passes through a prism or diffraction grating it shows up as individual lines of colors that correspond to the specific wavelengths emitted. This is a line spectrum. Each element produces its own unique line spectrum. Neon, when electrified, produces a set of wavelengths that look red when viewed together. Neon signs make use of this. If you look at white light through a prism or diffraction grating you see a rainbow of one color blending into the next, called a continuous spectrum.

Here are a couple of analogies that might help you better understand this. Imagine that you're jumping on a trampoline. The springs transfer energy to you and you move to a position of greater potential energy. However, you don't stay there because you're attracted to the earth by gravity. This makes your position unstable. When you fall back down the energy that you absorbed is returned to the springs when you hit the mat. Electrons in a substance absorb energy by being heated, having electric current passed through them or as a result of a chemical reaction. They're attracted to the nucleus of the atom as you're attracted to the ground. When they return to their lower energy position the absorbed energy is emitted as light just as your absorbed energy was emitted as motion and stretching of springs. 

To understand how emitted light is quantized, think of a stairway vs. an elevator. If you're in an elevator you can be in any position between floors. If you stop on a stairway there are only specific positions, the steps, that you can occupy. You can jump up two steps and back, or up three steps and back, but you're limited to the positions in which there's a step to occupy so the amount of energy you can expend jumping up is limited to specific amounts. Electrons are limited to specific distances from the nucleus so they absorb and release specific amounts of energy called quanta.