I was told that a WiFi AP re-modulates its radio signal in order to enable it to better go through obstacles and noisy places, reaching more distant client's transceivers this way. Basically, the receiver tells the transmitter to slow down to get the data more clearly. As a result the data rate slows down too. what exactly of a radio wave is re-modulated? Frequency, amplitude, or what? Could anyone also graphically represent a radio wave before it gets remodulated and after, when it carries less data?
I think you are talking about beamforming - it's not about modulating the signal itself but controlling the phases transmitted by the different parts of the antenna array. Ideally, the different phases add up to a maximum in the exact position of the receiver.
Another method for the radio to achieve a greater effective distance is to lower the transmission rate, so that even a weak signal is still decipherable. The slower rate may also use another modulation method but not necessarily.
Most 802.11 modes use quadrature amplitude modulation (QAM) which can get quite complex when modelled in practice.