your over complicating it (though it can be a complicated subject)
inputs can be thought of like a light switch, you turn it off or on, but you are not part of the loop (well you could be but that would be bad), instead of a switch the inputs are connected to transistors, which take very little current to change states (because they are very high impedance)
connect a input to +5 and the transistor switches on, connect it to ground and it switches off (it may be backwards I forget how they are arranged in the chip, doesnt really matter for this)
Since the transistor takes very little current to reach one state or the other due to its input impedance, if you left it unconnected it would wildly fluctuate as it picks up electrical energy from the air (RF interference, body capacitance whatever ... it actually makes an ok random number) so you need to "steer" (yea I dont like that term either) the pin to one state or another by using a pullup or pull down resistor
edit: and no you will find this type of setup on many digital electronics throughout the ages