When the switch is closed, it creates a direct connection to ground or VCC, but when the switch is open, the rest of the circuit would be left floating (i.e., it would have an indeterminate voltage). For a switch that connects to ground, a pull-up resistor ensures a well-defined voltage (i.e. VCC, or logical high) across the remainder of the circuit when the switch is open. Conversely, for a switch that connects to VCC, a pull-down resistor ensures a well-defined ground voltage (i.e. logical low) when the switch is open.
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