If you wanted an explanation, you should have asked for one. Otherwise,
we'll assume the answer is as obvious to you as it is to us.
Why you can't see anything:
Those wavelengths of light are called "infrared" because they are longer
wavelength (lower energy) than visible red. They are used for remote
controls *because* they are not visible to us, yet easily generated and
detected by silicon devices.
Why your camera sees it:
The camera uses a silicon-based detector, either CCD or CMOS. Silicon
is quite sensitive to near-IR, which is one thing that makes near-IR a
good choice for remote control communications. So the camera sensor
naturally sees the IR, unless the camera incorporates a really effective
IR filter to remove those wavelengths before they reach the sensor.
In fact, most digital cameras *do* have an IR filter, because IR is seen
as white light by the sensor (it passes through the RGB filters) which
reduces saturation and shifts colours. So there is an IR-blocking
filter which is effective enough at reducing the effect of IR naturally
present in scenes illuminated by the sun or incandescent lamps. But
it's not effective enough to *completely* block the very bright IR
produced by the LED in the remote control.
BTW, there are video cameras built for security/surveillance that
deliberately have high IR sensitivity so the camera plus a few IR LEDs
make a "see in complete darkness" camera.
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