While in a standard auction you have to pay your bid only if you win, in an all-pay auction you pay whether or not you win. The standard example is a dollar auction where you're selling a dollar. Bidding a penny to get a dollar seems reasonable, but someone else then might bid two cents. The bidding can keep going even past a dollar, and the more people fighting for the dollar the more the person selling it makes. Bidding-fee auctions are similar, where each bid you make costs money. You might remember Swoopo? They used to put up ads like "An iPad just sold for $21.32!" not mentioning that the participants overall had spent more than the retail cost of the iPad on bidding fees. Eventually people caught on and they went bankrupt.
In a less scammy vein, however, this is also how competitive prizes work. In the X-Prize teams spent over $100M in competition for a $10M prize. I can't find an estimate for how much people spent to win the $1M Netflix Prize but when you look at the number of people and number of teams it was probably well above $1M.
Could we use this for charity? Imagine a donor thought two charities were both excellent and had very similar returns, but they knew lots of other people strongly disagreed and preferred one or the other. By offering to donate $X to the charity that received the most in donations, could they move more than $X to the charity of their choice? It might be even better to make the criterion be the most independent donations of at least $Y, because getting more people to donate has value in terms of expected future donations.