This isn't really an electrical engineering question, but the short answer is that your eye has limitations. All light is a subclass of a larger form of energy called electromagnetic radiation.

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We can see the world around us because objects reflect light that our eyes can see and interpret as images. Light is electromagnetic radiation ranging from ultra-violet to the far infrared. The human eye only sees a portion of the full light spectrum, from about 400nm to 700nm.

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Usually we are not able to see infrared rays with our naked eyes. But we could see it when we watch it through a digital camera (or mobile camera). Why it happens?

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IR Illuminators provide IR light that enables true Day/Night day Security Cameras to capture clear images at night or in low-light. Infrared light is invisible to the human eye. True Day/Night security cameras are sensitive to IR light and can use it to capture images. Adding infrared light to a scene significantly improves the cameras performance in low light.

Your camera is based upon Si, which has a bandgap of 1.12 eV which means that for light that is ~ 1.1 u and shorter the camera can possibly detect it. This range of wavelengths is in the part of the spectrum called Near-IR. You eyes cannot see wavelengths LONGER than 720 nm. Near IR transmitters used in TV remotes etc. typically are 850 nm.

The IR Illuminator emits light in the infrared range of the electromagnetic radiation spectrum. With IR light, a scene that still looks dark to the human eye, is visible for security cameras with nighttime capabilities. The IR Illuminator’s LEDs act like a spot lights for the camera while remaining invisible to the naked eye.

At night or in other low light conditions 400-700nm light is lacking. Although humans cannot see infrared light beyond 700nm wavelength, camera sensors can. Adding 850nm infrared light to a scene significantly improves the cameras performance in low-light or at night.

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Light in the infrared spectrum has many advantages, it is invisible to humans so does not cause light pollution in areas where visible light would be obtrusive. Perpetrators often are not aware that they are being observed because it appears dark to their eyes. Images captured using infrared light are Black & White. Only white light has the wavelengths (400nm to 700nm) that our eyes see as color.

You can't see EM radiation with a wavelength shorter than around 730 nanometers, or what our brains perceive as red. However, your camera doesn't have the same limits, and will pick up the infrared light and try to display it just like any other light.