As always, your best starting move is to google "luminous intensity."
There, you can find the definition:
"Luminous intensity: candela (cd)
The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian."
It turns out that, in air, the frequency 540 x 10^12 Hz is about 555 nanometers - pretty much in the middle of the range of wavelengths seen by the human eye. Luminous intensity is a subjective descriptor taking into consideration the spectral (Photometric) response of the average human eye. {The comparable objective descriptor NOT taking into consideration the spectral response of the human eye is, "Radiant Intensity," in units of mw. per steradian (with no frequency/wavelength data involved), which is useful for IR or UV radiation, as well as visible radiation.}
The steradian is the unit of solid angle and is the angle subtended by an area r^2 on the inner surface of a sphere of radius r.
But your source does not have to illuminate the entire unit steradian to be measured. As a given amount of radiation is concentrated into a smaller and smaller solid angle with optics, the luminous intensity within that smaller solid angle increases. Thus, optics can increase the luminous intensity of an LED by concentrating the light emitted into a smaller solid angle, even though the total radiated optical power does not change. The result is increased brightness on-axis, but reduced brightness off-axis (as you see with the Mag-Lite). The Luminous Intensity of any sized beam of light can be determined by measuring the radiated power falling on a receiver with an arbitrary sensitive area and normalizing the result for the actual area (and distance from the source) of the receptor.
Unless you factor in the angle over which the LED spreads its radiation (reported as either the whole angle between half intensity points or the half angle from the central axis out to the half intensity point), you can't make a direct comparison of the total amount of optical radiation of two different LEDs, although you can compare the on-axis brightness to the eye of the two sources.
That doesn't make the luminous intensity useless. It is still a good indicator of how subjectively bright the source will look to the human eye. That is very useful if you know where the eye will be located relative to the axis of the LED as in, for example, a cockpit or dashboard display. It just won't be very useful (alone) in telling you how much light you can project onto an extended surface, as in the case of a "flashlight."
In fact, think of the on-axis brightness of a "Mag-Lite," as you change the focus by rotating the head. The luminous intensity can be greatly varied by changing the focus, but the total light emitted by the bulb and batteries does not change. Depends on what you want to do with the light.
awright