The graph to the right might represent some consumer's yearly demand for DVDs, almost certainly a normal good for most people. At a lower income her demand is the curve labeled DI1. On demand curve DI1, when the price of DVDs is US$10 she will buy 15 per year, but when the price is $25 she only buys 5 a year.
Suppose our consumer changes jobs to one where her salary is considerably higher. This increase in income would cause her demand for DVDs to increase (shift out) to the demand curve labeled DI2. Now that her income is higher, she demands more DVDs at every price. If DVDs sold for $10 each she would buy 30 in a year, while if they sold for $25 each she would buy 20 in a year. For her, DVDs are a normal good.
You may be asking yourself, are there any cases in which demand for a normal good will fall as income increases? The answer is an emphatic no, because the definition of a normal good is a good whose demand increases as income rises. If some consumer's demand for a good falls when income increases, then that good is not a normal good for that consumer in that income range.