Honor in Brief
Blizzard provided a lengthy explanation of Honor and PvP rewards quite a while ago, but documentation could be better, and there is still some confusion among players about exactly how the system works.
Honorable Kills - These are kills of players not more than 12(?) levels below your own level. In groups and raids, everyone in the group or raid gets credit for the kill. If multiple groups contribute to an honorable kill, everyone in all the groups get an Honorable Kill. Apart from a few NPC leaders such as Thrall or King Bronzebeard, you do not get any Honor from killing NPCs.
Dishonorable Kills - You do not, at this point, receive a Dishonorable Kill for taking out a player below you level range; you simply don't get an Honorable Kill for it. The only way to get a Dishonorable Kill at the moment is by killing NPC "civilian bystanders," essentially meaning certain NPCs that are not guards. Furthermore, there are no penalties associated with dishonor at this stage, unless you consider having your Dishonorable Kill counter go up a penalty.
Contribution Points - This is an experience-like credit that is based on your contribution to successful PvP battles. We know that damage dealt is part of the equation, and healers in the group that do no direct damage to the enemy are also factored in. It would appear that all nearby group members get some points, even if they have done nothing, as is the case with experience when fighting mobs. These points are more important than your Honorable Kill count, as it is your Contribution Points that will ultimately determine your PvP ranking, and hence whether you qualify for the rewards, which come in the form of special high-status items.
Obviously, this is an incentive-based system. You are rewarded for victory over enemy characters within your level range, but you are not deterred from killing players below your level range. While it may seem rather one-sided, disincentives are much more difficult to implement than incentives. For instance, the system has to be flexible enough to allow a high level character to defend themself against a swarm of players below their level range, which is a great deal more complicated than it sounds. Even the strict level limits on combat used by some MMORPGs are not without problems.
Let the Fight Begin
1.4 has affected PvP servers differently from Normal servers. On Normal servers you can't be attacked by another player unless you attack them first. PvP is initiated only by attacking enemy NPCs or manually turning on your PvP flag. Subsequently, PvP is entirely consensual on Normal servers. This doesn't mean that the opposing faction won't try to disrupt the enemy's questing by attacking key NPCs, merchants, and so on. Still, the impact of 1.4 on Normal servers has been relatively small.
On PvP servers, all players in Contested zones are flagged for PvP upon entering the zone. You start out in friendly zones like those on Normal servers, but at around level 20 most of the areas where you can gain further experience are Contested. At this point you can expect to start having encounters with the other faction, for better or worse.
PvP on a PvP Server
If you read the forums on the official site, you may well get the impression that questing on a PvP server has become impossible since the patch. Although there was a noticeable increase in PvP activity for a few days, this really isn't an accurate assessment of the situation. I have personally gained several levels on a PvP server since the system was introduced, much of it soloing outdoors, as have most of the players I know. After all, Azeroth is big world, including friendly territory and instances; locking down the opposite faction for any length of time is inconceivable. What's more, the death system is such that in most cases, players can escape the conflict by waiting a few minutes or making evasive maneuvres upon respawning.
To be sure, the environment is a little more hostile than it was before 1.4. Prior to this patch, it was not uncommon to see opposite factions in contested zones questing right beside each other, or even dancing with each other rather than fighting. While mildly amusing, it's not what most people on a PvP server signed up for. On the other hand, there are clearly players on PvP servers that are now discovering that they don't really belong there.
For what it's worth, I'm already seeing players above my level range ride right past me on the road again without bothering to kill me.