There are various types of freedom: political; economic; etc.
However, what was the freedom Paul was referring to in his letter to the Galatians? The answer is freedom from the "principle" of Law. Paul says that this is the freedom that every person receives and enjoys as a Christian.
What, however, is the problem with this law?
1. It awakens sinful desire – Romans 7:7-11.
Paul says that knowledge of the Law actually produces a greater desire for sin. Sin becomes more desirable once it is seen as "forbidden".
2.It produces guilt – v.19; Romans 7:18.
Knowledge of the Law produces tremendous guilt because now that we know what right is, we see what we do wrong and that triggers guilty feelings.
3. It produces a sense of hopelessness – v.16; Romans 7:24.
Knowledge of the Law and seeing how helpless we are to keep it produces a sense of either despair or cynicism.
We can't fully obey God, and this makes us feel hopeless, and frightened because of the consequences of this disobedience (James 2:9-19). When Paul therefore declares to the Galatians that they were free, he meant that as Christians they were now free from the curse of the "Law".
Christians had to obey human laws, taxes, social situations, but they were free from the principle of Law established by God. The question was - How?