"Floating diffusion", also called "sense node", is a region in active silicon (diffusion) region electrically isolated from all other nodes. It's a quasi-neutral region (i.e. it's not fully depleted) isolated by p-n junction from other nodes. There is no metal contacts to this region. Thus, it's potential is determined exclusively by the amount of charge stored in it, and its capacitance. Capacitance of this region is usually very low, to achieve high conversion gain, i.e. the change of its potential/voltage with the addition of one electron. It's potential can also be changed by swinging the voltage on neighboring nodes (i.e. gate of the reset transistor), due to capacitive coupling.
So, the "diffusion" comes from the fact that this region is located in Si diffusion. "Floating" means that it is not connected to any of the fixed/controlled voltage nodes, its potential is "floating".
Before the readout, the floating diffusion is reset (emptied of non-equilibrium carriers). During the readout, the electrons accumulated in the photodiode are transferred to the floating diffusion (by opening transfer gate). It's voltage changes, and this change is amplified by the source follower and read out.