Here's how I read it:
the resistance of a resistor is being modeled as
where is temperature in degrees C, and alpha is what is called the "temperature coefficient of resistance". is some initial resistance. It would, technically, be the resistance when the temperature is The resistance of a resistor changes with temperature, and here is one model for how it changes. The units of must be inverse degrees C in order to cancel out the units of . Otherwise, you wouldn't have units of Ohms on both sides. Hence the It would, perhaps, be better to write, for example,
Does this explanation clear things up?