t is the length of the ray as measured along the ray in units of the vector Rd. Ie., t=0 is the origin of the ray. t=1 is a point on the ray 1 Rd unit away from the origin (as measured along the ray), that is it is the length away from R0. is the point units away from R0 along the ray, and so forth.
To see this, look at each point separately. t = 1 means add Rd to R0. t=x means add a vector in the direction of Rd whose length is x times the length of Rd to R0. This is just generating all vectors of all positive lengths in the direction of Rd from R0.
Physically, you might say that the length of Rd is the "speed" with which a particle is travelling along the ray (for motivation, look at the derivative of this function with respect to t, where you interpret t as time). Mathematically, you may only be interested in Rd's that are unit vectors, so that the point corresponding to t = C is C units away from the origin R0.