Since a good healer cannot be defined by numbers as it is different in every encounter and far different depending on which classes are present as well as who is doing what here is a nice wall o' text. I don't know anything about you but this is assuming someone reading this has trouble with healing and wants to know what they are overlooking more than "if your recount is good and no one died you are gooood."
A good healer understands and anticipates incoming damage. In the same way the dps need to know what damage abilities are going to be used to avoid them (I.E rogue and whirlwind) a healer should understand the different damage patterns on every pull as well as possible over damage from dps not avoiding it (again whirlwind). In a new instance healing is purely reactionary unless you have researched every trash pull and after that healing is mainly proactive but a mix of reactionary as well due to RNG. The healer will also understand the differences in healing each type of tank.
Understanding each fight takes healing from 'omg their dying spam spam spam' to a calm rhythm and greatly improves efficiency. As one spell is being cast the next spell to two should already be decided based on anticipated damage. You have 1.5 seconds without haste to change your mind should something change. This should also include stop casting.
With that, a good healer understands all of their spells. They understand the effect of each spell on their HPS (as well as the hps of their combined spells working at once, if possible), heals per mana, how much can be expected from the average heal of that type, and how much extra healing a crit would bring, though it is never safe to count on a crit.
-note your HPS do not define your healing but rather it defines your maximum throughput of heals. In a fight that everything is going well your hps might sit at 1k, but when things go wrong you may sit around 3-4k hps. Knowing how to maximize this is important when a lot of damage is flying around but a healer should not be judged on their hps on any given fight unless it is evident that they are doing very little healing.
A good example would be the priest class which I play. In a high damage situation, having a Prayer of mending bouncing, while a renew is ticking on both tanks, circle of healing smacking 5 people and proccing an instant flash heal and a gheal bomb hitting the tank followed by that instant flash heal will generate an enormous amount of healing in the right situation, yet in the wrong situation would be horribly inefficient.-
A good healer will do their assigned job but still be aware of what the other healers jobs are and be able to pick up other players if that healer is lacking or maybe has to move to avoid damage. A living tank does nothing if all the dps is dead, and all the dpsing being alive is no good if the tank is dead. In an unassigned situation making sure the tanks don't die is number one priority but you should also consider your healing classes strengths. Obviously it doesn't make great sense for the pally to attempt to keep the whole raid up while the shaman heals the tank. People dying because the healing wasn't your assignment is only acceptable if your assignment was taking so much damage it would be impossible not to spam them. In that rare situation a polite "sorry but I had to chose you or the tank" is fine provided the group was not low due to your neglect (but if you let that dpser sit at 50% for 30 seconds and the tank was secure, you have failed).
In terms of player deaths it is always situational, but even with the best healers death happens. In an educated group of players unless you flat out failed (which happens though it should be rare. ex: your wife starts screaming at you) most people understand why they died. In a newbie group understanding incoming damage is even more important to prevent the next deaths and politely explaining what went wrong, especially in a non-accusing manner helps. A fictional example, "When the tank has 3 stacks ticking on him I have to spam big heals on him, if 8 of you stand in the aoe the entire time, someone will die." This way you haven't singled someone out and called them bad, potentially impacting the raid or leading to an argument which is a waste of time, while putting pressure on the group to do their job.
In some situations like the last boss of heroic nexus the damage taken meter will help prove your point if the group feels they are not failing, but are each taking more damage than the tank. I would use this lightly, but if one groups incoming damage feels completely different than the last this can be a good indicator of what is going wrong.
A good healer will always be prepared. Mainly typical in raiding guilds, but as a healer, enchants should be and imo, are required. I have two healed in raids during which I did 80% of the healing and the other healer was baffled because we had comparable gear. After going through his gems and enchants he was missing 200+ healing, 20 mp5, 250 mana, etc just from his enchants as well as having some stam gems, /gasp. If you want to be able to carry inexperienced groups enchants are 100% necessary and if you go oom at 2% and wipe and are unenchanted it is YOUR fault regardless of how bad the group is.
In a raid environment flask and buff food should be required as well. Sometimes your gems, enchants, and flasks are not necessary but when people make mistakes, especially double pulling, this can be the difference between no one dying and wiping. When you save groups from definite would be wipes consistently you will start to build a reputation for being a great healer and good players will pursue you and trust you. Bad players will as well, but the great part of being a healer is being able to pick and choose your groups.
As you improve you will know you are doing so when each tank you group with consistently messages you afterwards, and some, will refuse to run without you unless another of their trusted healers is online. At that point you can pick and chose your dps as you wish.
In terms of comparing healers there really isn't much comparing of great healers and if there is it is usually minor points coming down to style rather than skill. A great healer is a great healer and you will always feel comfortable in a raid with them, and hopefully they will challenge your own skills.
In terms of good healers it usually comes down to "well he heals well, but he always dies in the fire." It is even more important for you to avoid damage than any other classes. You can have the best timing and judgment in terms of heals, but if you are so absorbed with peoples health bars that you don't move when on flame wave and wipe the raid, or cause the other healer to show his skill and one heal the rest, you are not a great healer. Granted death happens, and sometimes incoming damage is timed horribly with what is happening with the tank, but you should always do your best to avoid taking damage.
-Also, if you get hit for 4k it is again important to know incoming damage. I've seen too many healers top them self off and the tank dies when it wasn't necessary. At the same time you shouldn't let yourself sit at 60% health.
In short a good healer, understands his class and each of their spells and uses them as efficiently as possible, how their regen works and exploits it to a T, is prepared, adapts quickly, is very aware, learns damage quickly and anticipates it the next time, stop casts, educates their group (since you have the clearest picture of damage floating around), and most of all, is not afraid to say "that was my fault." In the end this translates to "Group never dies."