Can someone explain the use of the transistor in this circuit?
It doesn't work.

The transistor is in a common-base configuration, which provides no current gain at all (actually very slightly less than unity). All of the current from the pullup must pass through the open-collector uC pin, along with the bias current flowing through R1.

The transistor simply functions as a one-way current gate. It's slightly better than an ordinary diode in the sense that its forward drop (VCE) when conducting is on the order of 200-300 mV, instead of the 600-700 mV of a diode. This helps with the noise margin on the one-wire bus.

A better configuration would be common-emitter, with the base resistor connected to the uC pin, but then the pin would have to be configured as totem-pole (drives high as well as low) and the polarity of the signal would have to be inverted &mdash; the bus is pulled low when the pin is high. In this configuration, you would be able to have a pullup that the uC couldn't handle directly.

An N-channel MOSFET would work even better with regard to the noise margin (in either circuit configuration).