Please give me brief description about the polygamy in Islam? As the polygamy is opposed or criticised by the modern world, what can be the best answer given to such opposers or criticisers?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

For an answer to your question about polygamy please read Fatwas no.: 81505, 81469 and 81436.
1- It is known that the number of women outnumber that of men. This is undeniable reality. If every man contents himself with only one woman, then there will remain a huge number of women without experiencing marital life. As a result they will be deprived of having offspring. Likewise, they will be denied satisfying their sexual instincts legally, on which Allah has created the humans. Dissatisfaction of sexual instincts. This in turn might lead the women to taking refuge in what Allah has forbidden or befalling in the claws of the criminals, or getting lost in the distasteful meanness.
2- The growth and development of a generation that believes in the Oneness of Allah the Exalted, and stands for the evolution of the earth and the succession in it.
3- Sometimes a man marries a pious woman, but happens to be barren. If Allah has not legislated the marriage with a second one, then there will be only two ways before this man: either he divorces his wife, an act which he might not want to do, or he would hold her without having any children who cause his happiness in this world and with whom he would profit in the hereafter.
There are some other benefits that are the essential fruit of the legislation from All-Knowing and All-Wise. Here I would like to point out that Allah when permitting the man to have polygyny, He did not leave him unbound, but restricted him with certain rules and regulations that guarantee His rights to all, and at the same time these regulations stop the transgressor at his limit. It is the method adopted by All-Knowing, All-Wise in His legislation.
I hope these benefits - what we left are more though - are sufficient to justify the legality/lawfulness to the polygyny, and to convince the one who has a heart or gives his ear while he is heedful.
And it is our turn now to ask you: ' Tell us please, who are more unjust concerning the right of women: Are they those who call her to the legislation of Allah, in which she can enjoy justice, security, chastity, and other benefits in her favor in general, and in this matter of polygyny in particular, or are her rights fulfilled by those who merchandise on her behalf exposing her, calling her to filthiness, preventing her from superiority, beautifying the vice for her, making her loathe the beautiful, and finally throwing her in the snare of adultery and debauchery? They are however, preventing her from marrying a polygamist, and making such kind of marriage abominable in her views. At the same time they are allowing fornication for her, and beautifying it (before her). As a result she is deprived from joining the family convoy and living under the family shade.
Eventually, when she becomes pregnant, she does not find any body who can take care of her, and reduce her trouble. And when she gives birth to a baby, she finds himself/herself an orphan by birth, an absolute orphan! And she alone suffers for the child's education, expenses and his nourishing.
On the other hand, the child also lives shouldering the burden of orphanage, craving for the respect of parenthood and the honor of legal relation/lineage.
Which of the two is more unjust? The answer is perhaps clear.
Allah knows best.