Step 1: Recall what whitewash is made of.
Whitewashing uses a runny paste of slaked lime, calcium hydroxide, $\text{Ca(OH)}_2$, brushed onto the wall.
Step 2: Think about what the wall is exposed to afterwards.
Once painted, the wall sits in open air, and air always carries a small amount of carbon dioxide gas that can slowly react with the coating.
Step 3: Write the slow reaction that follows. \[ \text{Ca(OH)}_2 + \text{CO}_2 \to \text{CaCO}_3 + \text{H}_2\text{O} \] Over two to three days, this reaction quietly converts the calcium hydroxide layer into a thin, hard coating of calcium carbonate.
Step 4: Explain the shine.
This newly formed calcium carbonate layer is crystalline and reflects light well, which is exactly what gives freshly whitewashed walls their glossy finish after a few days. \[ \boxed{\text{Calcium carbonate}} \]