LED lights are very different from incandescent lights and fluorescent lights. Fluorescent lights work by ionizing mercury vapor in a glass tube. This causes UV light to be created which is then converted into standard visible light using a phosphor coating that is on the inside of the tube. This also means that it is very dangerous if you break a fluorescent tube by accident because you will be exposing yourself and others around you to mercury, so make sure that if this does happen, to clean it up very carefully. Incandescent lights have a filament inside the bulb that is composed of ductile tungsten, which is a chemical element of atomic number 74, and located in a gas-filled bulb. When an electric current passes through the filament, it heats up to a temperature that produces light, but also produces a lot of heat. LED lights however are a two-lead semiconductor light source. It is a p-n junction (a boundary or interface between two types of semiconductor material) diode, which emits light when activated. So when a suitable voltage is applied to the leads, the electrons are able to recombine with the electron holes within the device, and then they release energy in the form of photons.
LED lights are so bright because they have a high lumen/watt score. Lumens are the measure of the total quantity of visible light emitted. Here is an illustration that demonstrates the difference between a low lumen count and a high lumen count.
The reason that LED lights appear so much more bright is because if you were to put a 40W incandescent bulb against a 40.5W LED bulb the difference between the number of lumens (light output) would be 3,550! With the incandescent bulb producing only 450 Lm and the LED bulb producing 4,000 Lm. This is an enormous difference between the levels of light you are getting from each bulb and because the LED bulb is so much higher there is no way that you would need to replace a 40W incandescent bulb with the equivalent Watt in a LED. Instead, you could drop down to a 5-8W LED bulb to get the equivalent but since your power usage is so much lower it would make sense to upgrade to a 9-12W and just about double the amount of lumens you are receiving for less than half the energy. Below is a chart from Wikipedia that shows the comparison between incandescent, fluorescent, and LED lights to give you a rough idea of how they compare in terms of energy usage and lumen output.
Since there is such an enormous difference between LED bulbs and incandescent bulbs and also a difference between fluorescent lighting and LED’s it’s not hard to figure out that the reasons that LED lights seem so much brighter is because they have a higher lumens output/watt which means that even though less power is being used more light is being produced instead of being wasted on heat loss.