What is the relationship between solubility and precipitation?
I'll relate it all the stress. See Below
Solubility is like how much stress you can take during the day. A little stress and you are ok....a lot of stress and you start to get stressed out (but still ok). This is solubility. When you put ions into solution, the solution can hold the ions in an aqueous state and they are said to be soluble.
At some point, you can't take anymore stress - one extra bit of stress and you will crack/explode/break down, etc. At this point, if we are talking about ions, you are saturated. You have the maximum amount of ions in solution and you can't fit anymore.
If you add one more stress, everything falls apart! You have a breakdown. This is when you have a saturated solution and you add a bit more of the ions, they will fall out of solution and precipitate. At this point you've exceeded your solubility and precipitation has begun. Anymore ions you add will precipitate.
Maybe that helps with the larger concept. There are equations and such, but this is the broad conceptual idea.