In the book of Galatians in the New Testament, when Paul is speaking to the people of Galatia about following the old laws, or the Jewish law, he is speaking of the body of Jewish laws that govern even the smallest aspects of the lives of the Jewish faith/culture, not just circumcision or eating kosher. The Jewish law refers to 613 mitzvot, or commandments. These commandments are referred to...
...collectively as the "Law of Moses," "Mosaic Law", or simply "the Law".
These laws referred to "instructions" that provide guidance in terms of the things they should do, and laws against the things they should not do. The laws are divided specifically in terms of the "positive" laws—248: based on "the number of bones and significant organs in the human body;" and, the "negative" laws—365: based upon "the number of days in a solar year." Of the negative laws, there were three that Jewish law suggested "One should let himself be killed rather than violate…" including worshipping idols, practicing "unclean" or "abominable" sexual acts (as outlined in Leviticus), or murder.
These laws governed the actions of the Jews throughout the day and year: what one would do upon waking, the foods that were acceptable to eat ("kosher"), how to dress, how to handle business transactions, guidelines for choosing a mate, and the observance of Jewish holidays, to mention a few.
This set of rules and practices is known as halakhah.
Paul means the entire Jewish law. There was some argument in the early church that new Gentile Christians should be bound by the Mosaic law including the rite of circumcision, which represented the covenant between God and the Jews. While circumcision represented the covenant, the Jewish end of the covenant was the observance of the Law. This argument originated because almost all early Christians were Jewish; it was Paul who first carried the Gospel to the Gentiles.
Paul had argued in Romans that becoming a Christian freed him from the law. His argument here is that there is no difference between Jew and Gentile, or as he put it, Jew and Greek; if one is a Christian then the purpose of the law had been fulfilled by the sacrificial death of Jesus; therefore the Jewish law in its entirety no longer applied. In essence, he means that Gentile Christians are not "honorary Jews."