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This is extremely difficult because our eyes and brains are not innately made to understand properties at the quantum level. The dual nature of light is what you are referring to. This means that light behaves as a particle and a wave. The wave is typically easier to comprehend as the crests and troughs drawn on the board. However, when light interacts with individual atoms like in the photoelectric effect it behaves as a singular particle called a photon.
I am not going to pretend like I completely understand the concept of light (because I'm still pretty confused by it), but in class Professor Lavelle described photons as being discrete packets (or quanta) of electromagnetic energy that simultaneously act like waves and particles. Though photons are often treated as particles, and the photoelectric effect gives evidence that light exhibits behaviors of particles, photons can also be calculated to have frequencies, wavelengths, amplitudes, and other properties of waves. Light behavior can be represented by wave functions that convey the probability of finding a particle at a given place/time. Basically, the probability of a photon being at a given point is a wave, exhibiting properties inherent in wave mechanics, but a photon itself is not a wave.
I had this question too and still do, but I have come to some understanding that our model for light is still debated on. In a large scale sense, our wave model of light works for our use in physics and larger chemistry, however when coming down to particle side such unique phenomena where intensity does not change the electron's ability to be dislodged (photoelectric experiment) it becomes clear that light also exhibits interesting behavior only understood by specific quanta of energy, otherwise as photons. In larger quantum mechanics light is still difficult to be modeled as the duality of light is thought to often be a combination of both, only a wave form, or perhaps nothing of both! In the end, we need to check our resolution of the problem to understand which model to use and realize that photons are a packet of energy, which can exhibit wave form dynamics on a large scale.
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