Sibling rivalry is simply a consistent conflict between brothers, sisters, or brothers and sisters. Some degree of sibling rivalry is normal: "Researchers studying sibling relationships during middle childhood (ages approximately 5-11) most often find that the majority of sibling relationships during this time can be described as ambivalent with a real love-hate feel," according to parenthood.com. Having their children fighting is often a bigger worry for the parents than it is for the kids themselves.

These rivalries are often caused because children feel that they are competing with their siblings for parents' attention or for their identity (which sibling is better at a sport or has more talent in a field, etc.). They can also be a convenient outlet for other stresses in the kids' lives -- the sibling is just available to fight with when the child is already in a bad mood. Sometimes parents' interference, trying to make the children "play nice," yelling at the one who "started it," or protecting the younger child, actually makes things worse; advice is given in many places not to force the siblings to do things together so as not to breed resentment. On the other hand, making sure the kids get equal amounts of attention from their parents and one is not praised over the other is supposed to help keep the rivalry to a minimum. To quote Dr. Vera Rabie-Azoory, "If you stand back and try to appreciate what each one has separately -- and, it's not an easy thing to do. It's not to say that you love each one in their own special way. That's just words. You have to be really careful to be honestly, inside yourself, internally impartial, to love what this one does and what that one does for their own sake."

Kidshealth.org recommends getting some kind of professional help only if there is risk of severe physical or emotional harm to one of the siblings, if the rivalry may be related to depression or some other problem which would be worth treating on its own, or if the fighting is causing marital problems in the family's adults.

Nonetheless, rivalry and the love/hate relationships can continue into adulthood and continue to influence family interaction, especially when siblings need to deal with issues about their aging parents' care, or are constantly comparing their own adult achievements to their siblings'.

(Note: the author of this writeup is not a parent and grew up as an only child -- my personal experience with sibling rivalry comes from my younger half-brother and half-sister.)

Sources:
http://www.parenthoodweb.com/parent_cfmfiles/pros.cfm/317
http://www.parallaxweb.com/parenting/sibriv.html
http://my.webmd.com/content/article/1700.50681
http://kidshealth.org/parent/emotions/feelings/sibling_rivalry.html
http://kidshealth.org/parent/emotions/feelings/sibling_rivalry_p4.html