The first main factor that explains the negative relationship between price and quantity where demand is concerned is the income affect: As the price of a good or service rises, it takes up a larger proportion of the consumers income. In other words, the opportunity cost of the good (the next best alternative foregone) has increased, leading fewer consumers to buy the good/consumers to buy less of the good. This explains why as price of the good rises, the quantity demanded falls.
The second main factors is the effect of diminishing utility. If we define utility as the satisfaction that a consumer achieves when they buy the good, the more of the good they buy, the less utility they gain from each extra unit consumed. A good way to explain this is using Mars Bars: If I buy one mars bar I may be willing to pay the same price for a second as it will give me an equal satisfaction. However, after 4 Mars Bars I will begin to feel sick and would not be willing to pay the same price for a 5th. This explains how the more of a good is consumed, the less consumers are willing to pay for another (Marginal price begins to fall). This again explains the downward sloping demand curve.