Dominance is a CP characteristic that you can add to in order to decide the rankings of your wolves.

The male/female with the highest dominance in your pack take the place of alpha male and female, and these two are the only ones that are able to breed together within your pack (you can still stud out your males or breed your females to other pack's males).

The male/female with the second highest amount of dominance will take the place of beta male and female. There isn't really any special advantage to being a beta, they just have that title near their name.

Every other wolf is an omega!

Edit: The images that are assigned to a wolf by default can be changed regardless of status/gender. For example, if you have a male pup, you can have his image display with the alpha female pose. The poses are really just preference ^^