Present value refers to the future value of an asset that has been discounted back to its value in "today's" dollars (or other economic unit).
When we talk about present value, we are referring to the "reverse compounded" value, or discounted value as of today, of a future payment or stream of payments. To do this, we take that future value and discount it by an assumed rate to determine what it would be worth today if it earned that rate of return in the interim.
For instance, in the realm of investing for the future, you might want to know how much you would have to invest today, at a designated assumed rate of return, in order to end up with a set amount at some future point in time. As an example, if you wanted to have $10,000 available to you in 10 years' time, and we assume it will grow at an average annual compound rate of 10%, you would have to invest approximately $3,850 today. So $3,850 is the present value of $10,000, earning 10% compounded annually over the next 10 years.
The present value method is also called the discounted cash flow method.
A different way to look at it: As James Early, now advisor of Motley Fool Income Investor, explained in a 2004 article, present value has to do with $100 now and $113 a year from now. If he offers you either $100 now or $100 a year from now what are you going to take. D'uh. $100 now. The present value of money has to do with how much he will need to offer 12 months hence to get you to consider waiting rather than taking the $100 and running.
You'll take into account things like how much you could get if you put $100 into Treasuries for a year and how likely you think it is that James will show up a year from now with the promised money. In the article, James lays out the math of working the formula into the future.