Hierarchy is very important to rabbits; in the wild it is necessary to keep the peace in a large warren and domestic rabbits are also hierarchical, amongst themselves and with us...
Like all animals used to living in large groups, hierarchy is of paramount importance to rabbits - very necessary to keep the peace in a large warren. In the wild, rabbits live in male/female pairs and usually within a family group, with one pair or family being at the top of the tree and other pairs/families subordinate to it. This is the best way to ensure survival of the warren by producing the optimum number of litters who survive to adulthood. Newcomers or young rabbits not yet established in a pair are not readily accepted and tend to live a fairly miserable life on the outskirts of the warren.
Domestic rabbits live best in neutered male/female pairs and still adhere to this need for a firm hierarchy.
Sizing up the competition
The first thought in a rabbit's mind when encountering another rabbit is "are you superior or inferior to me?" Classic signs of dominance are mounting (this can be done by either a male or female), chasing, circling and, if the other rabbit doesn't submit, nipping and fur pulling. If the 'inferior' rabbit submits by laying its head on the ground, the show of dominance may continue for a good while longer, sometimes even weeks, so great is a rabbit's need to establish its place once and for all in the hierarchy.
Rabbits do sometimes approach each other as equals but once bonded one rabbit - nearly always the female - will always rise to the top, even if in a very gentle, easy-to-miss manner. Other rabbits may take an instant dislike to each other and immediately start a proper fight, scratching and biting hard enough to draw blood, but this is very unusual in neutered male/female introductions.
Once the hierarchy is established, the 'top bunny' enjoys certain privileges, the most noticeable of which is grooming. A top bunny will request grooming from a subordinate by laying her head flat on the ground close to the other rabbit, often pushing her head under his chin. She may return the favour at times as an act of affection but generally speaking the top bunny gets much more grooming from her subordinate(s).
Confusingly, rabbits also lay their heads on the ground to show submission and you may often see subordinate rabbits doing this but the usual response from top bunny is either to ignore or give a quick ear or eye lick.
The top bunny also has "first dibs" on food and may chase off any rabbit who she feels is threatening her food, in particular if it is a treat food such as a piece of carrot or banana. She may also expect her subordinate(s) to "keep guard" for her while she sleeps; for example, she may completely relax and roll on her side or back to sleep while her subordinate(s) remain in the "loaf" position (legs tucked under body, eyes half open - the classic rabbit sleeping postion).
Hierarchy and humans
How the humans of the house fit into this hierarchy is less clear. On one level, we may be seen as subordinates to the top bunny, but on another level we are, of course, the overall boss - dictating when meal times, nail clipping, litter tray cleaning etc takes place. In other words, there are certain elements of her life that top bunny cannot control and is happy to leave to us. However, when it comes to simple interaction with our rabbits, we are included in the hierarchy. Most top bunnies see themselves as superior to us and request grooming from us in the same way they would from another rabbit. Others may groom their humans by licking their hands, feet and face but this is more likely to be a sign of affection rather than an acknowledgement of inferiority. Subordinate rabbits are usually very happy to accept grooming from us but do not demand it in the way a top bunny would.
When interacting with your rabbits, it is important to be aware of this hierarchy and not do anything to upset it. For example, if top bunny feels her subordinate(s) are getting too much attention or grooming from us, she may become jealous and this may adversely affect their relationship. On the other hand, you don't want the subordinate(s) to feel neglected so the safest thing is to treat each rabbit equally but when in doubt groom top bunny first - this is what she and her subordinate(s) expect.