To what were the Galatians being moved?

To another gospel.

Paul had preached the grace of God in Christ to the Galatians. After Paul left Galatia, the Judaizers came to the Galatians with their "gospel" of keeping the Jewish Law. The Judaizers were Jews who had been converted to Christianity. They believed that in order to become a true Christian the Gentiles had to be converted to Judaism and keep the Law of Moses. The males had to be circumcised.

The Book of Galatians is Paul's answer to teachers who would attempt to include all or any part of the Law of Moses in the Gospel of Christ.

Let us keep in mind that the new covenant is the writing of the Torah, the Law, in the mind and heart of the believer; not the letter of the Law of Moses but the eternal moral law of God. It is not that we ever forsake the moral law of God. Rather it is true that we change from the outward observance of the Law (that which Paul was discussing) to the development of the fullness of the Law, the Torah, in our heart. Christ is the fulfillment of the Law and the embodiment of the Law. As Christ is formed in us the Law is formed in us. This is the new covenant.

When referring to the Law we are speaking primarily of the Ten Commandments but also of the additional statutes and ordinances.

Each of the numerous commandments of the Law, including the keeping of the Sabbath, refers to a universe of attitudes and behaviors. All of these attitudes and behaviors taken together compose the eternal moral law of God. Jesus Christ is Himself the fullness of the eternal moral law of God. In Him we can observe all that the Law is, all that the Law desires and commands, the fullness of the expectation of God concerning His creatures. (from A Study Guide for the Book of Galatians)