Three pieces of information from the comments:
- It fizzed and disappeared in vinegar.
- It had a yellow-orange color in blue flame.
- It's salty (note that it's usually a bad idea to taste random stuff you find on your floor).
The only white crystalline material that is a plausible candidate for being there and fizzes in acetic acid (ie vinegar) is calcite - $\ce{CaCO3}$. It's also a mineral that has 'retrograde solubility' meaning it dissolves more readily in cold water. This is probably how it got to the water in the first place. This is also why it precipitates on your electric kettle. It is the same stuff.
The salty stuff that burns yellow-orange is obviously $\ce{NaCl}$, aka table salt. It also probably dissolved with the vinegar as well. Why is the salty taste not quite like table salt? Well, first of all it is mixed with calcite. But, calcite has no taste. It's possible that there is some $\ce{KCl}$ or $\ce{MgCl2}$ in there as well. They are slightly more bitter than $\ce{NaCl}$. This is the stuff they use in low sodium salt.
There's another possibility - it could be any of the epsom salt family, $\ce{MgSO4.$n$\,H2O}$.
As to would this be dissolved in the first place, you can only speculate. You say that it came from a table that was outside. Did people eat there? Could people had spilled salt on it? Is the airborne dust in your area contain a lot of calcite? What about your basement? Could someone have spilled some salts on the floor, maybe even years ago?