Modern candles are designed to burn with a constant flame as the candle burns down. But back in Shakespeare's time, as the candle burned, the wick became longer and the flame larger, consuming the wax too quickly. To prevent this, the wick was periodically "snuffed", or trimmed. A candle was said to be "in snuff" when the wick needed trimming. Demetrius is saying that Starveling can't go into his lantern because it's "in snuff" and the flame would burn him. 

There's also a double meaning to this line; "in snuff" also meant to be irritated. Starveling is in snuff because they keep interrupting his speech.