From a coach's perspective...
HR does all the things mantioned above, but it does so much more. So many little things that the "average" guy doesn't know and really, doesn't need to know.
Early season things like increase capilaries, increase in golgi apparatus, increase in CO2 clearance. Late season things like increase in VO2 max, Increase LT/AT, Ability to stay in a higher zone longer.
The thing about HR zones and training is the testing and the communication betweent he coach and athlete. the coach can crunch the numbers and post the athletes zones, but the athlete has to comunincate back to the coach how they feel when in those zones.
Examples:
Athlete A: Athlete A is doing interval sessions where the athlete is doing longer sets of AT training (A later season workout.) The athlete is supposed to stay in zone high 3, low 4 for the entire lt session, say 8 minutes. Athlete A reports back to the coach that no matter how hard he tries, he cannot get into zone 4. His legs tire and he just does not have it.
The coach has a couple choices.
1) The athleles zones are set to high and the coach is asking the athlete to work to hard.
2) The athlete is overtrained.
3) The athlete is dogging it.
Athelte B: Athlete B is doing a long ride on Saturday and is told to stay in zone 2. He is told that it is OK to have your HR climb during the climbs, but should try and get back to zone 2 within a few minutes of the increased exertion. The athlete does the workout and reports back to the coach that he was having trouble staying in the aero position and that he was having a hard time keeping his HR lowno matter how slow he went.
The coach has a couple choices.
1) The athlete has improved enough to warrant retesting.
2) The athlete is a super human and only wants to train at race pace.
3) The coach has set the numbers to low.
These are real examples. Both of these athletes are mine and this what I did.
Athlete A: He reported to me that he could not get his HR into an LT. I spoke with the athete and looked at his log. I looked back at what he had been doing and if he had been able to get into the zone prior and if he was able to stay there. In the past he was able to get into the zone and spend time there. he had been reporting poor sleeping habits for the last few days and his log was FULL of workouts. He was clearly overtrained. He was given 2 days completely off and 3 days off reduced workouts. He has since retested and is happy with the new numbers. This athlete will find himslef on the podium a lot this year.
Athelte B: Athlete B called me on saturday afternoon and told me that he almost fell off his bike and that he felt like he wasted a whole day. Again I looked back at his schedule and noticed that he had complained about hte same type of thing prior. (I originally thought he was a superhuman.) However after this latest workout we decided that he needed an increase in HR zones. He was increased 5 beats in each zone and has been reporting good workouts. He has not retested as he is in a build phase and I do not want to interupt it. He will retest in 2 weeks. I want to mention that his increase was because of his willingness to stay in those zones. He test fantastic and his numbers were right when he started but has increase his fitness so fast that retesting every week is pointless.
The season is early and it is crucial, especially on the bike to set your numbers and follow them. Of course this is only important if you want to have a good season.

Sheldon
Sorry for the typos and spelling errors, I'm at work and don't have time to proof read this.