The physical data interface of USB is simpler (only two signalling wires, D+, D- instead of the two differential pairs for firewire). Supply of power to the devices is simpler (+5V instead of >20V with firewire, which needs an additional DC/DC converter on the device). For most primitive low-speed devices (mice, keyboards, toy rocket launchers) the data transfer implementation is simpler (see e.g. the bit-banging software-only V-USB implementation for microcontrollers).

So on the low-performance side, the advantage is clear. And end-users like the simplicity of having the same physical port for all their computer peripherals (which can use low- (<1Mbit), full (12MBit) or high (480MBit) speed, without the user knowing or noticing).

While I personally think that Firewire is the more elegant, better performing and more flexible communication technology, I can see why USB surpassed it in the marketplace.