The statement "financial analysis requires an explicit consideration of the time value of money" refers to the variations in relative value over a given period of time as money accrues interest or, conversely, loses value because of the effects of inflation.
Inflation has historically been the single greatest determinant of the value of money over time. The simplist way to look at this is by considering the price of an item of food 30 years ago, and then comparing it with the cost of the same item today. Factoring in the rates of inflation over that period of time will illustrate the degree to which the value of the dollar has diminished. A candy bar that cost ten cents 40 years ago costs a dollar today. That means your money buys less quantity today than it did yesterday. The dollar is worth less in relative terms.
Individuals often make decisions regarding the most profitable way to increase the value of their money. Many will attempt to calculate the amount their savings will accrue over a certain number of years if kept in a bank and compare that with estimate growth in value of their money if they invest it in the stock market or buy a Certificate of Deposit.