In course of evolution (possibly), mammary glands became vestigial in male mammals, but became fully developed in females. Is there any plausible explanation for this characteristic?
It comes down to investment in offspring. Males invest little in offspring only a little sperm whilst females have to develop the more expensive egg and the energy used through its development. In the mammalian line, this investment has increased in amount, initially through viviparity and then through the secretion of feeding fluids.
In species, such as humans, where there is a lasting pair bond and both male and female invest in rearing the young then I suppose there could be a situation where it makes equal sense for both males and females to nurse - although the cost of mammaries on other functions may favour specialisation anyway - but remember that, in many mammals, it is the mother alone that rears the offspring.
You may also find the answer to this question useful: Do any birds beside the family Columbidae (or any reptile or mammal) feed their young “Crop Milk”. What I hadn't realised is that there actually two species of bats where the male lactates.
The mammary glands in human males is not vestigial but rudimentary.
Human females have XX chromosomes and males have XY chromosome,here the "Y" chromosome is provided by father and "X" by the mother. At the time of fertilization, the father can provide either X or Y chromosome. If he provides Y chromosome the child will be male and if he provides X then child will be female. The mother always provides X chromosome. So the Y chromosome in the male child is responsible for the development of male sex organs and due to the presence of X chromosome the female sex organs are suppressed. Note that the female organs are suppressed but they are not eliminated. At the time of puberty males don't receive hormones which initiate the development of female sex organs. As a result the mammary glands stay in males as nipples but the hormone effects are only present in females and cause the formation of large amounts of fatty tissue near the nipples and develop as breasts.
A distinguishing characteristic of the class Mammalia is the presence of mammary glands. The mammary glands are modified sweat glands that produce milk, which is used to feed the young for some time after birth. Only mammals produce milk. Mammary glands are most obvious in humans, as the female human body stores large amounts of fatty tissue near the nipples, resulting in prominent breasts. http://en.wikipedia.org/wiki/Female
While estrogens are present in both men and women, they are usually present at significantly higher levels in women of reproductive age. They promote the development of female secondary sexual characteristics, such as breasts. http://en.wikipedia.org/wiki/Estrogen