The explanation in the book is overtly simplistic. Increase in supply actually lowers prices for multiple reasons not just by affecting people’s subjective valuation of the final margin good consumed (eg more supply usually means there are more sellers and hence more competition), but value of the margin good is affected as well.
This is because value depends on marginal utility. For example, nobody has an absolute value for water. In Sahara desert where there is no water a wandering water merchant can demand a small fortune for a cup of water.
However, the more cups of water you have the less you will be willing to pay for it. The first cup of water that saves your life will have huge value for you. The second might still be valuable, but the value of each next cup will start dropping rapidly. Whereas you might be willing to pay fortune for the first cup of water a 30th cup of water will have almost no value. If you are drowning in a middle of a lake additional cup of drinkable water would have absolutely no or possibly even negative value as more water would just bring you disutility.
This is because, generally speaking, people’s utility of consuming most products is (at least locally) concave. That means generally each additional unit consumed brings less benefit than the last one.
Note this does not mean people have less demand for the product. Demand is the relationship between price and quantity people want to consume. Something that is not very valuable (eg water in modern western city) might be demanded and consumed at high quantities.
Next the book is being too simplistic. Value of something just determines your reservation price/willingness to pay (highest price you would be willing to pay for a good). However, in competitive markets consumers usually pay less then their reservation price as competition between suppliers brings prices down further. Higher supply usually implies there are more competitors in the market (although not always as existing firms can just scale up production as well).