I was wondering, basicly every radio-transsmission works with electromagnetic waves which travels at the same speed whether I modulate the information with a low frequency or high frequency such as done with LI-FI. What makes Li-fi faster? what makes any wireless transmission faster/slower if eventually I send my information with electromagnetic wave which travels at the same speed? What makes lifi special?
The wave propagation speed is only relevant when you start approaching the theoretical limit of that type of wave's ability to transmit information.
For an analogy, consider people having a conversation in a room full of air. They're using sound waves to transmit information. The speed at which those waves propagate is the same for every speaker, in that particular medium. Does that imply that everyone transmits information at the same speed?
The answer is no, of course not. The information is overlaid on the sound wave in a particular way, and we call that speech. You can transmit the same information at the same speed across a wide range of frequencies. You can speak faster or slower without varying the pitch of your voice. (In fact, some people can transmit speech faster than you can receive it.) You can use different languages that might allow you to communicate particular ideas at different rates.
The theoretical maximum speed at which information can be transmitted via audible speech is only loosely related to the speed of propagation of an audio wave. Put the same conversation underwater and the waves propagate four or five times faster but you don't even notice because the time required for the wave to propagate is so many orders of magnitude less than the time required to encode and decode a single datum.
Digital signals using EM waves are a much more specialized technology, compared to the human systems that enable verbal communication. But we're still far from any theoretical limit on the rate at which EM waves could possibly transmit information. Each of the 802.11 protocols used by your Wi-Fi device has a theoretical maximum bitrate, based on multiple elements of its design. At one point those were measured in Mb/s, now they're measured in Gb/s and there's plenty of room to keep going. A question over on Physics SE asks about the upper limit for fiber optics (which also use EM waves, of course) and you can see from the answers that, at Gb/s for Wi-Fi or Li-Fi, we're still many orders of magnitude away from hitting a ceiling on transfer speeds.
That's why the wave propagation speed isn't as meaningful as you expect. As far as what makes Li-Fi faster than Wi-Fi, I'm not even sure that's the case in isolation; practically speaking, what seems to be driving the development of the former is over-saturation of the frequencies used by the latter. That's more of an issue of congestion than anything else, which means that if Li-Fi had been developed first, the situation might be reversed, and popular science mags might be writing the same BS headlines about Wi-Fi instead.
"Wireless at light speed." Give me a break.