Thus if you are a rich person trying to donate a lot of money to a truly good cause the charity will sometimes be forced to refuse your money despite needing it - just to keep the IRS away. To get around this they will match, thus ensuring that plenty of little donors to keep the IRS away from the charity while allowing them to make the large donation they were planning on making. These are always structured with the hope to give the full amount, so if you are planning on a small donation it is to your advantage to donate during a match since otherwise your charity might not get as much from the rich person.
Note that none of the above applies to politics where there are laws in place limiting total donations per person that a match cannot get around.