It has to do with "being on the floor". The din is really to sit on the floor. Anywhere within 3 tefachim of the floor, (I think 12 inches) is considered part of the floor.
The gemora in many places speaks of a "mourners bed". Being that in that society all sitting and leaning were done on beds, the beds were higher, hence the need for a "mourners bed", one that is lower and close to the ground. Remember however, that this is still a "bed" and bound to be as comfortable as one.
I don't have exact sources, but regarding the mourners bed, the Artscroll Kinnos mentions it in the footnotes in relation to a kinnah that says everyone had to make their own mourners bed. In a regular society, the comforters would prepare the mourners bed for the mourners. However, by the churban EVERYONE was a mourner and therefore everyone had to prepare their own.