Are you familiar with the movie Encino Man? This movie, while probably not award-winning, is at least a Generation Y-defining movie that you have probably watched countless times on basic cable. We'll see how this movie is going to help us understand an apparent paradox of light... 
...or more precisely, electromagnetic radiation. (N.b. this is an expanded version of an introductory physics electromagnetic waves presentation.) 
First, consider all types of "light."
The electromagnetic spectrum encompasses all types of "light," here listed from short to long wavelengths. Notice that visible light is only a very small portion of the entire electromagnetic spectrum, which we perceive as colors. T he vast majority of the electromagnetic spectrum is invisible to our eyes, but we can detect their presence indirectly with certain instruments, or even different parts of our bodies. (When discussing all types of "light," we'll use "electromagnetic radiation," as often "light" refers only to visible light.) Let's introduce these types of light...oops, electromagnetic radiation, from short to long wavelength.
Hulk smash, well, because of being exposed to gamma rays. More scientifically, gamma rays are the shortest wavelength form of electromagnetic radiation, and a single gamma ray photon is the most energetic and dangerous to be exposed to. The progression of our discussion is introduce longer and longer wavelengths of electromagnetic radiation, which will be comprised of lower and lower energy photons. This form of electromagnetic radiation cannot be seen by our eyes, but can certainly cause damage to molecules, especially those in our bodies, so while exposure to gamma rays may not cause you to transform into the Hulk, it may cause irreparable damage to your cells. 
Slightly longer in wavelength, and lower in photon energy are x-rays, which again cannot be seen by our eyes (well, maybe for Superman), but can be made visible with special devices or certain materials. Note that tissue is relatively transparent to x-rays, while bone, and especially metals are opaque. (What is that thing in this person's nose?)
Still longer in wavelength on the electromagnetic spectrum, we still cannot directly "see" ultraviolet, but can detect it with special devices, or in this case, materials that react in certain ways to being ultraviolet exposure, such as our skin, or this Milky WayTM candy bar. 
"Who was Count Dooku's Jedi Mentor?"
So either children are supposed be Star Wars trivia experts, or have to go to a nightclub with "blacklights" in order to answer this correctly... (Video link: "090529-1090772.")
Then slightly longer in wavelength on the electromagnetic spectrum is visible light, the only type of "light" we can directly see with our eyes. (What is this person looking at?)
Slightly longer in wavelength along the electromagnetic spectrum, we're back again to types of "light" we cannot directly see with our eyes--in this case, infrared, also known as "heat waves," which our eyes cannot directly see (but we can indirectly feel), but certain devices allow us to "see" in the infrared. (Video link: "infrared heat cam.")
The longest wavelengths along the electromagnetic spectrum are collectively known as radio waves, which are subdivided into microwave, TV, FM and AM bands depending on the type of device used to send and receive these forms of electromagnetic radiation.
Second, let's further explore the different terms we've been using to describe electromagnetic radiation--wavelengths and photons.
Electromagnetic radiation can be described as having wave properties--it can be thought of as spreading out in all directions from a source, much like circular ripples from a rock thrown in a pond. Different types of electromagnetic radiation wavelengths merely have different spacings between their ripples as they spread out through space. Keep in mind that this is a very crude visualization of this behavior, but an effective one nonetheless.
Electromagnetic radiation can also be described as having particle properties--it can be thought of on the smallest scale as packets of energy traveling through space--these are photons. Different types of electromagnetic radiation photons merely have different energies, and some are less energetic or more energetic (and potentially hazardous to you). Yes, this is also a very crude visualization of this behavior, but we have to give Trekkies equal time as Star Wars fanboys and fangirls.
So this leads us to a key question: how can electromagnetic radiation--"light"--be both a wave, and a particle. This graphic here (an "ambigram") is one perhaps an oversimplification of how this can simultaneously have two mutually exclusive properties, but let's delve into the wave-particle duality next.
Third, wave-particle duality, in terms of the movie Encino Man. 
For those of you who somehow haven't seen this movie, let's recap. Sean Astin and Pauly Shore are high schoolers who discover a caveman (Brendan Fraser) frozen in ice. The caveman is unfrozen, and just doesn't understand the modern world. Hijinks ensue. 
Let's think about updating this movie--suppose caveman is found and unfrozen behind our school. You want to take him for a ride in your car, but he freaks out. "It's okay, it's just a car--see, caaaar," you reassure him, but he freaks out at a truck parked next to your car. "Yes, that's kind of like a car, too," you generalize, "see--made of metal, tire, windows. Car, car, car." You take him out to the nearby road, and let him watch traffic for a while, and he gets what a "car" is.
Then you point to a bird flying overhead, and tell him, "see, bird--biiiird." And he says, "I'm not a dumbass, I know what a bird is, I just didn't know your word for it." Apparently the caveman is also picking up on sarcasm. 
So now you want more hijinks, and decide to take the caveman to Disneyland. Somehow you get him through airport security without him having a valid ID, and he's waiting at the gate, and he's looking out through the window at the runway, and he's looking, he says, "car." It's the biggest car he's ever seen, and not only that, he starts watching as it goes by and then right up into the air, and he says, "bird!" "Car-bird!" 
But the caveman is not watching something that is both a "car" and a "bird," but an airplane, which has the attributes of a car (made of metal, with tires and windows) and attributes of a bird (flying in the sky). 
So think about the car-bird duality of airplanes. An airplane is not merely a car, nor a bird, but shares attributes of both a car and a bird, which only seem mutually exclusive until we imaging wrapping our minds around experiencing an airplane for the first time.
And now think about the wave-particle duality of electromagnetic radiation. Light is not merely a wave, nor a bird, but shares attributes of both a wave and a particle, which only seem mutually exclusive until we try wrapping our minds around the nature of light for the first time. When you wonder about wave-particle duality works, think about car-bird duality.
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