Okay kiddo, have you ever tried to dissolve sugar in water? Did it work? That's what we call solubility - how well something can dissolve in a liquid.
Now, imagine you have a bunch of different things and you want to know which ones will dissolve in water and which won't. A solubility table is like a cheat sheet that tells you which things dissolve easily, which ones take a bit more effort to dissolve, and which ones won't dissolve at all.
The table usually lists different substances (like salt, sugar, and baking soda), and then tells you how much of that substance can dissolve in a certain amount of water at a certain temperature.
So if you wanted to know if salt would dissolve in water, you could look on the solubility table and see that at room temperature, up to 35 grams of salt can dissolve in 100 mL of water.
The solubility table helps scientists and people in different industries (like medicine or manufacturing) figure out how to mix different substances together or separate them out. Pretty cool, huh?