I'm not entirely positive on my understanding of this or if my explanation will make sense (because it takes a little bit of a physics background), but here goes:
Friction is a resisting force. Force= mass x acceleration. Now, heat is a type of energy that usually gets released when one type of energy becomes another type. In the physics of motion, the two main types of energy are potential and kinetic. Potential is usually due to position and kinetic is due to motion.
Since the total energy is conserved when there's a transformation of energy, the amount of potential energy (U sub i) and the amount of kinetic energy (K sub i) before the transformation is the same as the amount of potential energy (U sub f) and kinetic energy (K sub f) after the transformation.
Acceleration is the derivative of velocity, both being vectors related to rates of change in position or the rate of the rate of change in position, in the case of acceleration. Kinetic energy has to do with velocity so I imagine the fact that friction is a force (meaning it has an acceleration, meaning it has a velocity) means that there's a transformation in energy and, when that transformation occurs, heat is given off.
Does that make sense?
Essentially, friction causes potential energy to become kinetic energy and this transformation gives off heat, not unlike when energy in a chemical equation needs to balance out so heat is either absorbed or given off.