Where does "tables" mean in this sentence?
It means what it normally means:
a piece of furniture with a flat top and one or more legs, providing a level surface on which objects may be placed, and that can be used for such purposes as eating, writing, working, or playing games.
There is some anthropomorphism in talking about them "groaning". The imagery is comparing a person whose is holding up so much that they are struggling and groaning, to tables being close to the most they can hold up (and possibly bending under the strain, and making a noise doing so).