The command to circumcise:
Genesis 17:10, 12 This [is] my covenant, which ye shall keep, between me and you and thy seed after thee; Every man child among you shall be circumcised. And he that is eight days old shall be circumcised among you, every man child in your generations, he that is born in the house, or bought with money of any stranger, which [is] not of thy seed. 

The purpose of circumcision:
As men again departed from God, the Lord chose Abraham, of whom He declared, "Abraham obeyed My voice, and kept My charge, My commandments, My statutes, and My laws." Genesis 26:5. To him was given the rite of circumcision, which was a sign that those who received it were devoted to the service of God--a pledge that they would remain separate from idolatry, and would obey the law of God.

At this time the rite of circumcision was given to Abraham as "a seal of the righteousness of the faith which he had yet being uncircumcised." Romans 4:11. It was to be observed by the patriarch and his descendants as a token that they were devoted to the service of God and thus separated from idolaters, and that God accepted them as His peculiar treasure.By this rite they were pledged to fulfill, on their part, the conditions of the covenant made with Abraham. They were not to contract marriages with the heathen; for by so doing they would lose their reverence for God and His holy law; they would be tempted to engage in the sinful practices of other nations, and would be seduced into idolatry.  {PP 138.1}

If man had kept the law of God, as given to Adam after his fall, preserved by Noah, and observed by Abraham, there would have been no necessity for the ordinance of circumcision. {PP 364.2} 

He then required of Abraham and his seed, circumcision, which was a circle cut in the flesh, as a token that God had cut them out and separated them from all nations as his peculiar treasure. By this sign they solemnly pledged themselves that they would not intermarry with other nations; for by so doing they would lose their reverence for God and his holy law, and would become like the idolatrous nations around them.  {1SP 262.3} 

By the act of circumcision they solemnly agreed to fulfill on their part the conditions of the covenant made with Abraham, to be separate from all nations, and to be perfect. {1SP 262.4} 

What is circumcision to us after Jesus Christ died on the cross?
circumcision or uncircumcision was nothing. {6BC 1111.2}

1 Corinthians 7:19 Circumcision is nothing, and uncircumcision is nothing, but the keeping of the commandments of God. 

"There is neither Greek nor Jew, circumcision nor uncircumcision" (Colossians 3:11)

"After the decision of the council at Jerusalem concerning this question, many were still of this opinion, but did not then push their opposition any farther. The council had, on that occasion, decided that the converts from the Jewish church might observe the ordinances of the Mosaic law if they chose, while those ordinances should not be made obligatory upon converts from the Gentiles. The opposing class now took advantage of this, to urge a distinction between the observers of the ceremonial law and those who did not observe it, holding that the latter were farther from God than the former.  {6BC 1111.1} 

Paul's indignation was stirred. His voice was raised in stern rebuke: "If ye be circumcised, Christ shall profit you nothing." The party maintaining that Christianity was valueless without circumcision arrayed themselves against the apostle, and he had to meet them in every church which he founded or visited: in Jerusalem, Antioch, Galatia, Corinth, Ephesus, and Rome. God urged him out to the great work of preaching Christ, and Him crucified; circumcision or uncircumcision was nothing. {6BC 1111.2}

Not required by God but only to avoid prejudice of the Jews:
Paul, with his usual good judgment, caused Timothy to be circumcised; not that God required it, but in order to remove from the minds of the Jews an obstacle to Timothy’s ministration. Paul was to labor from place to place in the synagogues, and there to preach Christ. If his companion should be known as an uncircumcised heathen, the work of both would be greatly hindered by the prejudice and bigotry of the people, The apostle everywhere met a storm of persecution. He desired to bring the Jews to Christianity, and sought, as far as was consistent with the faith, to remove every pretext for opposition. Yet while he conceded this much to Jewish prejudice, his faith and teachings declared that circumcision or uncircumcision was nothing, but the gospel of Christ was everything. { LP 73.2 }

If one is not circumcise, can he still be considered as a Jew?
Romans 2:29 But he [is] a Jew, which is one inwardly; and circumcision [is that] of the heart, in the spirit, [and] not in the letter; whose praise [is] not of men, but of God.

Colossians 2:11 In whom also ye are circumcised with the circumcision made without hands, in putting off the body of the sins of the flesh by the circumcision of Christ:

What is the real essence circumcision?
Obedience: Deuteronomy  10:12-13, 16 And now, Israel, what doth the LORD thy God require of thee, but to fear the LORD thy God, to walk in all his ways, and to love him, and to serve the LORD thy God with all thy heart and with all thy soul,  To keep the commandments of the LORD, and his statutes, which I command thee this day for thy good?   Circumcise therefore the foreskin of your heart, and be no more stiffnecked.

Deuteronomy  30:6 And the LORD thy God will circumcise thine heart, and the heart of thy seed, to love the LORD thy God with all thine heart, and with all thy soul, that thou mayest live.

Jeremiah 4:4 Circumcise yourselves to the LORD, and take away the foreskins of your heart, ye men of Judah and inhabitants of Jerusalem: lest my fury come forth like fire, and burn that none can quench [it], because of the evil of your doings. 

What is the real essence of uncircumcision?
Disobedience: Acts  7:51 Ye stiffnecked and uncircumcised in heart and ears, ye do always resist the Holy Ghost: as your fathers [did], so [do] ye.