The discount rate is (1) An interest rate used to bring future values into the present when considering the time value of money. (2) The interest rate the Federal Reserve (the Fed) charges to loan money to banks.
For investors, the discount rate is the rate at which dollars in the future are brought back to the present. This is very closely tied to the time value of money, so reading that page is worth your while.
A brief example, however, for those in a rush.
If you have $100 today, it is worth $100 today. (Mr. Obviousman strikes again!) However, how much is $100 two years from now worth today? Inflation, at least, should make it obvious that it will be less than $100 today, but how much less? The answer depends on the discount rate.
The discount rate is essentially the interest rate it will take to turn today's money into tomorrow's value, except the math is run in the other direction. So, if you expected to earn 5% on your money, how much should you invest today in order to have $100 two years from now? The answer is $100 / 1.05 / 1.05 = $90.70. That is, if you deposit $90.70 into a bank account that is paying 5% per year, you will have $100 in two years ($90.70 * 1.05 * 1.05 = $100).
Said in the other direction, using discount rate of 5% to bring $100 back to the present means that the $100 is worth $90.70 today.
Different discount rates give different present values and it should be obvious that the larger the discount rate, the lower the value in today's dollars.
Different investors calculate the discount rate differently. For example, Warren Buffett is said to use the yield on the 10-year US treasury bond + 5%. Other people calculate a discount rate using the weighted average cost of capital.
When determining a discount rate, some investors like to increase it for more risky securities, such as small cap stocks, where the future cash flows are more likely to be volatile.