Reserve units move in the Exploitation phase, which is otherwise forbidden for non-mechanized units to move in. So it allows you to do a 1-2 whack at a stack of strong defenders.
E.g. Madrid, stacked with 4-6 units can be a complete bear to take for the Nationalists if the Rep. are constantly able to repl units/reinforce into it. But if they can attack it at fairly high odds (hard, admittedly, with the -2L) in the regular combat phase, then release 1-2 stacks of reserves for a follow-up attack at hopefully good odds (given the step losses the Rep. will have incurred in the first combat), then they have the potential to take the hex in 1 turn...or at the very least, inflict a huge number of step losses that simply can't be replaced in one turn.
The same applies for attacks against the Northern zone, where almost all of the defenders are single steps. Hit Gijon at 3:1 odds in the first combat phase, knock off some steps (and greatly reducing its defense strength), then commit a stack of strong reserves (CTV, etc) and you should take Gijon that turn before any RPs or reinforcements can buffer it.
IMO, the Nationalist player MUST know how to use his reserves to win against relatively equal player skill...