Question: I studied the solubility of compounds in water. I have found that [calcium carbonate](http://en.wikipedia.org/wiki/Calcium_carbonate) doesn't dissolve in water. The teacher stated that the ionic compounds dissolve in water except some carbonates. What would be a clear elaboration of this phenomenon?

Answer: 
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> Teacher stated that the ionic compounds dissolve in water except some carbonates.
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That is, at best, an oversimplification. Other ionic compounds such as silver sulfide are sparingly soluble in water. Note that this isn't a carbonate. 

And sodium hydrogen carbonate - $\ce{NaHCO3}$ - is soluble in water. 

Sodium carbonate ($\ce{Na2CO3}$) is also soluble in water. 

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> I want a clear elaboration of this phenomenon can somebody help me??
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Solubility depends on:

1) The strength of the intermolecular attractions within the solute and the strength of the solvent-solvent interactions. How strongly is the calcium ion and the carbonate ion bound together? You might *think* that the force of attraction between a +2 and a -2 ion is strong, but remember, covalent bonds are generally stronger than ionic interactions. How strong are the solvent-solvent molecule interactions - which must be broken before something can be solvated? 

2) Solvation. How well can the solvent lower the energy of the dissociated solute ions? How well can calcium ion and carbonate ion be solvated (by water in this case?) How strong are the solvent-solute ion interactions? What about the entropy of solvation? (Solvation shells are highly ordered). 

If you wish to predict the solubility of some compound, try using hard soft acid/base theory.
To be very honest with you, it's almost impossible to predict accurately, the solubility of compounds. At the end of the day, it's best to memorize them. Yes, there are some cases wherein a certain logic or reasoning can be used, but mostly its better to just memorize the thing. As Abel said, it comes down to a difficult interplay of lattice enthalpy, and hydration energy.