As each player participates in Realm vs. Realm Combat (RvR), they accumulate Realm Points, which give them Realm Ranks and Levels. As each Realm Level is reached, the player earns points that they can use to receive new Abilities. These Realm Abilities are focused on RvR, and give your character different options and strategies for dealing with enemy players (and sometimes monsters).
Your character can rise in Realm Ranks and Realm Levels. There are 100 Realm levels, which are divided into 10 Realm Ranks. For the Realm Ability system, each player will receive one Realm Skill Point for each Realm Level attained - giving the player a maximum of about 100 points to spend on these new abilities.
In order to "spend" Realm Ability Points on a skill, you'll go to your standard class trainer. The Realm Abilities available to your class will be listed there. Please note that you do not have to have a high number of Realm Levels to be able to take advantage of these new abilities - in almost all cases, a character that has just a few realm levels can purchase at least a couple of new abilities.
There are two types of realm abilities: Passive and Active. Passive realm abilities are always on, and can affect your character in small ways, generally 3% per level (high levels of passive realm abilities grant substantial bonuses, however). Active abilities have re-use timers between 5 and 30 minutes, and are either instant effects or duration effects lasting between 30 and 60 seconds. Each class has a list of abilities tailored to them, and each class has an ability unique to them.
Some realm abilities have multiple levels, and each level will add more bonus. For example, the Augmented Strength realm ability awards 6 Strength points per level of the ability purchased, and there are five levels. So, in our example, a Level 3 Augmented Strength would give +18 Strength to a character.
The costs for each level of ability, as well as the advanced abilities increase with the level you are trying to attain. Also, please note that some Realm Abilities have pre-requisites that must be purchased before you can buy them. Pre-requisite skills may have to be purchased to a given level before an advanced skill can be trained.
See the Realm Abilities page for the list of all realm abilities.