Off-hand I can think of 5 species of highly intelligent and social matriarchal animals: Elephants, Sperm Whales, Lions, Hyenas, and one species of Baboon.
It appears that matriarchy is a form of society in which power is with the women and especially with the mothers of a community. Matriarchy is distinct from matrilineality, where children are identified in terms of their mother rather than their father, and extended families and tribal alliances form along female blood-lines. For instance, in Jewish Halakhic tradition only a person born of a Jewish mother is automatically considered Jewish. Hence Jewish descent is passed on from the mother to the child.
Matriarchy is also distinct from matrilocality, which some anthropologists use to describe societies where maternal authority is prominent in domestic relations, owing to the husband joining the wife's family, rather than the wife moving to the husband's village or tribe, such that she is supported by her extended family, and husbands tend to be more socially isolated.
Matriarchy is a combination of these factors; it includes matrilineality and matrilocality. But what is most important is the fact that women are in charge for the distribution of goods for the clan and, especially, the sources of nourishment, fields and food. This characteristic feature sees every clan member dependent beyond matrilineality and matrilocality and grants women such a strong position that these societies are now considered matriarchal.
The unclear concept of matriarchy, and of its replacement by "patriarchy" can be linked to the historical "inevitabilities" which the nineteenth century's concept of progress through cultural evolution introduced into anthropology. Friedrich Engels, among others, formed the notion that some primitive peoples did not grasp the link between sexual intercourse and pregnancy. They therefore had no clear notion of paternity, according to this hypothesis; women produced children mysteriously, without necessary links to the man or men they had sex with. When men discovered paternity, according to the hypothesis, they acted to claim power to monopolize women and claim children as their own offspring. The move from primitive matriarchy to patriarchy was a step forward for human knowledge.
This belief system was the result of errors in early ethnography, which in return was the result of unsophisticated methods of field work. When strangers arrive and start asking where babies come from, the urge to respond imaginatively is hard to resist, as Margaret Mead discovered in Samoa. In fact, while prior to the discovery of egg cells and genetics there have been many different explanations of the mechanics of pregnancy and the relative contributions of either sex, no human group, however primitive, is unaware of the link between intercourse and pregnancy. The fact that each child has one unique father has come more recently, however; Greek and Roman writers thought that the seed of two men might both contribute to the character of the child. By the time these mistakes were corrected in anthropology, however, the idea that a matriarchy had once existed had been picked up on in comparative religion and archaeology, and was used as the basis of new hypotheses that were unrelated to the postulated ignorance of primitive people about paternity.
One of the most persistent claims of feminist historians who concentrate in ancient and pre-historic societies has been the rebuttal of a possibility to a matriarchal society anytime in the distant past. It seems to be a way for them to legitimize their feminist research by distancing themselves from such outrageous extremities. On the other hand, several popular writers, like Riane Eisler, have energetically promoted ideas of an ancient Great Goddess, and the matriarchal society which worshipped her. Some archaeologists, like Marija Gimbutas and Lucy Goodison, have also contributed to the science of old goddesses by digging up and interpreting prehistoric finds from a new perspective.
It is unfortunate that the discussion of a possibility for female dominance in prehistoric or early historic societies has to be so strongly ideologically colored. First of all, there is no reason for even ardent feminists to take either positive or negative view into the question on ideological reasons. The oppression of women in many present-day societies remains the same even if patriarchy is proved universal, thus the need for improvement in women's status is as urgent were there any matriarchal societies in the past or not. Maybe anti-feminists feel like gaining ideological ground if it is proved that males have always been dominant. On that ground it could be seen as a biological necessity, but the logic is so weak that I wish to steer away from such argumentation.