Acidic and alkaline salt solutions: why do some salt form acid/bases while others don't
Without trying to go into too much detail this has a two part answer. 

First a salt by definition has an anion and a cation. So ordinary table salt, $\ce{NaCl}$ is a chemical salt, but table sugar is not a salt. So lets think of the cation as $\ce{C^+}$ and the anion as $\ce{A^-}$.

So we start out with solid salt which in chemistry is written as $\ce{CA_{(s)}}$. When the salt dissolves the two ions are hydrated which means that water molecules surround each ion and separate the pair. the chemical reaction is written like this: $$\ce{CA_{(s)} -&gt; C^+_{(aq)} + A^-_{(aq)}}$$

Typically the (aq) subscripts are left off, but implied. 

The second part of the answer involves the nature of the cation or anion. To understand if the pH of the solution will change depends on whether the cation is able to "donate" a hydrogen ion, or the anion is able to accept one. 

$\ce{NH_4^+}$ is a cation and is able to donate a hydrogen ion to the solution. So the pH will drop and the solution becomes more acidic. $$\ce{NH_4^+ + H_2O -&gt; NH_3 + H_3O^+}$$ 

$\ce{CO_3^{2-}}$ is a anion and is able to accept a hydrogen ion from the solution. So the pH will increase and the solution becomes more basic. $$\ce{CO_3^{2-} +H_2O-&gt; HCO_3^- + OH^-}$$ 

When water, $\ce{H_2O}$, makes or breaks bonds the process is called hydrolysis.