Translation:There are no chairs by these tables.
Maybe some examples will help?
A férfi a széken ül - The man sits on the chair (with the Hungarian -n ending for "on"). Chairs are viewed as basically flat things with a surface rather than an interior, so you sit "on" them.
A férfi a széknél ül - The man sits by the chair (not on it).
A tányér az asztalon van - The plate is on the table. Again, the table it flat, so things can be on it.
A férfi az asztalnál ül - The man sits at [or by] the table.
A férfi az asztalon ül - The man sits on the table - an unusual behavior.
And for good measure:
Az asztal a férfinél van - The table is by the man (or possibly in his possession - basically, the table is in the same general location the man is.)
Az asztal a férfin van - The table is on the man. Possible, but unlikely. Perhaps it is a small table and he is wearing it like a hat. Or perhaps it is a big table and we should hurry to get it off of him.
A szék is that usually four-legged piece of furniture with a seat and a back rest, what you'd usually call "chair" in English. A "seat" is somewhat more general - basically any place that's intended for sitting - and has its own word in Hungarian: ülés. (From ül, "to sit", and the suffix -ás/-és, which turns the action into a noun, literally "(the) sitting".)