The meaning of HIGH (in reference to a pin) is somewhat different depending on whether a pin is set to an INPUT or OUTPUT. When a pin is configured as an INPUT with pinMode(), and read with digitalRead(), the Z-Uno will report HIGH if a voltage greater than 2 volts is present at the pin.
A pin may also be configured as an INPUT with pinMode(), and subsequently made HIGH with digitalWrite(). This will enable the internal 20K pullup resistors, which will pull up the input pin to a HIGH reading unless it is pulled LOW by external circuitry. This is how INPUT_PULLUP works and is described below in more detail.
When a pin is configured to OUTPUT with pinMode(), and set to HIGH with digitalWrite(), the pin is at 3.3 volts. In this state it can source current, e.g. light an LED that is connected through a series resistor to ground.