Light is absorbed by electrons. When an electron absorbs light, the electron is raised to a higher energy state. The electron has to start and end at specific energies, though. Some atoms may not allow the electron to stay in the higher energy level, so the electron drops back to the lower energy and the light just gets re-emitted.

Here's an analogy. Let's say you've got a boat in the ocean. The water is excited by energy, creating waves. As waves come and go, the boat rises and falls, but it doesn't absorb any energy from the ocean. No useful work is done because the boat always ends up at the same place it started. Now if the boat is near a short cliff, a large wave might raise the boat high enough to leave it on top of the cliff. This is a high-energy state since it takes work to lift a boat against gravity. (If the boat suddenly came tumbling down, we'd see how much energy was "stored" by the big crash at the bottom!) Since it takes work to lift a boat out of the water, we see that the boat has absorbed some energy from the wave. (The wave is then slightly weakened, because energy is conserved.)

Light is the same way. Light could be absorbed and excite an electron to a higher energy state, but unless there's a place to park the electron at the higher energy, the electrons give back their energy and the light just passes on through.