This star represents what is known as a replacement note. When a printing error occurs during a normal press run and renders a set of bills unusable, replacement notes are used instead. With replacements notes, a set of serial numbers can still have the proper number of bills even if some of the original bills had to be pulled. The replacement notes have a sequence of their own, using the star as their final "letter." This allows for 99,999,999 possible replacement notes for any given bank, series and denomination. This should be more than enough: According to the Paper Money Collecting FAQ, there's about one error in every 100,000 U.S. Bills.
In general, replacement notes aren't worth more than regular bills. However, if you find a replacement note with a particularly interesting serial number -- like 00000001 or 999999999 -- or a large number of consecutively numbered replacement notes that you keep together as a lot, you may have a collector's item on your hands. Anything in the world is only worth as much as someone is prepared to pay for it and if the sequence of numbers means something to someone, they may be prepared to pay a lot of money for it or at least slightly more than the original value.
The value of the note also depends upon the condition and age of it. If it is in extremely good condition and is also very old, it will be worth considerably more money. Unfortunately, for the majority of the time, the bill will have no extra value. There is no harm in keeping it in the hope that the value will rise but it is extremely unlikely.
In general, replacement notes aren't worth more than regular bills. However, if you find a replacement note with a particularly interesting serial number -- like 00000001 or 999999999 -- or a large number of consecutively numbered replacement notes that you keep together as a lot, you may have a collector's item on your hands. Anything in the world is only worth as much as someone is prepared to pay for it and if the sequence of numbers means something to someone, they may be prepared to pay a lot of money for it or at least slightly more than the original value.
The value of the note also depends upon the condition and age of it. If it is in extremely good condition and is also very old, it will be worth considerably more money. Unfortunately, for the majority of the time, the bill will have no extra value. There is no harm in keeping it in the hope that the value will rise but it is extremely unlikely.
