Connecting power supply to fan? Does it work?
The battery holder is for 4 AA cells, which are 1.5V for alkaline, or 1.2V for NiMH. That's either 6V or 4.8V in total. The fan is a 12V. It may work at the lower voltage, though it won't blow very hard. AndrejaKo suggests to use a second set of 4 AAs to get to 12V, but you better get a 12V DC wall wart. Make sure it's DC! The 100mA the fan uses will drain your batteries in a day.
The white dingus is a connector, which you would use with a mating part, which you probably don't have. So you can cut it off, and solder the wires directly together.