Given that a certain amount of irradiance arrives as the surface point x, from the ωi\omega_iωi direction, we want to know what the radiance exiting that same surface point in the direction ωr\omega_rωr would be. This depends on the properties of the material and the reflection function (BDRF, discussed in the next slide). Some materials may be more reflective (larger differential radiance exiting) or less reflective (smaller differential radiance exiting).
For reflection at a point, is it possible for the outgoing radiance to be in multiple directions (i.e. multiple rays)?
Edit: after watching further, I believe this is explained in the next few slides. The BRDF takes in an incoming direction and an outgoing direction, and tells you how much light is going in that outgoing direction. This allows an incoming ray to be diffused over an area of the hemisphere.