Read this whole thread for a comprehensive explanation:
http://www.axisandallies.org/forums/index.php?topic=7927.0
In a nutshell, bidding helps to even out the playing field. If you played on a soccer team and always beat another soccer team by a large margin, you might “spot the other team 2 goals” to even up the playing field.
Bidding accomplishes the same thing in axis and allies. The team that (almost) always wins without a bid is the Allies. So the Axis are spotted some extra money at the start of the game to help even up the sides. They can either use that money to immediately purchase units and place them on the board before the game even starts, or they can save the money and add it to one or both of the axis’ coffers.
How much money is spotted is up to the players. Hence a “bid” format was created where player A and player B both bid to play the axis with $X extra. Whoever bid LESS (less money going to the axis) gets to play the axis with that money.
Eg. Player A “I’ll play the axis with 8 IPC extra.”
Player B “I’ll play the axis with 6 IPC extra.”
Player A “You’re nuts! The 6 IPC is not enough extra IPC to win as the axis. I’ll let you play the axis with your extra 6 IPC and I’ll blow you out of the water with the Allies. Game On!”
