Triclinium is the latin word for dining room, it also means the room where there are three couches where the rich people would lie down on (paint me like your french girl position) and eat and have parties. I don't know exactly what the common people had for eating, but I doubt they had the same as the richer folks.

I highly doubted that because eating is such a big part of our lives, it is almost impossible that they hadn't created furniture for it or even have a permanent space to eat.