Genesis 17:12-14 meaning

Every male among you was to be circumcised who is eight days old. So far, the institution of circumcision includes who is to be circumcised, where one is to be circumcised, and why one is to be circumcised. Now we are told "when" one is to be circumcised. The circumcision of the male child is connected with the purification of his mother, who remains unclean for seven days after the birth (Leviticus 12:1-4). Also, medically, clotting agents are not optimized before the first eight days; vitamin K is formed during the fifth through seventh day. Therefore, the eighth day is the first safe day for this procedure. Through modern medicine, we know "prothrombin" (which facilitates clotting) is below normal until the eighth day when it peaks. 

The sign of God's covenant was not directed just to sons and family, but to whole households, even a servant who is born…or who is bought…shall surely be circumcised. The firstborn son has the same obligation in the covenant as the lowest servant. Thus shall My covenant be in your flesh as a physical sign of an everlasting covenant. God's promised blessing extended to everyone. The fact that it extended to slaves who might have come from other lands is an early fulfillment of God's promise to Abraham that all the families of the earth would be blessed in him (Genesis 12:3).

In the New Covenant, physical circumcision ceased as a required practice among Gentile Believers. This was decided in the Jerusalem Council of Acts 15. However, the believing Pharisees, or some people like them who argued at that council that Gentiles did need to be circumcised, apparently did not heed the Council's decision. The letters of Paul to the Romans and to the Galatians directly addressed competing Jewish "authorities" who were teaching those believers that they did need to be circumcised and obey the Jewish law.  Accordingly, there is much about this subject in Paul's letters. Another example occurs in Philippians chapter 3. The apostle Paul states that the true circumcision are those who place their trust in God and worship in Spirit, while the false circumcision are those who place their trust in their physical circumcision (and related actions.)

Circumcision was not optional for Abraham and his descendents. If a father failed to fulfill his duty on the eighth day after his son's birth, the responsibility fell upon the individual himself to be circumcised when he reached maturity or that person shall be cut off. He that is not himself "cut" (circumcised) will be "cut off." The text here does not make it clear how an uncircumcised male was to be cut off from his people. It is likely that it means they would physically be cut off from their people. What is clear is that everyone who deliberately excludes himself cannot be a beneficiary of the covenant blessings and thereby dooms himself. 
Failure to be circumcised means that the violator had broken My covenant (Exodus 4:24-26; Galatians 5:2-4). By not becoming circumcised the person was rejecting God himself. Circumcision distinguished those who believed in God's promises to Abraham from those who did not.