Believers in Jesus Christ have many spiritual freedoms because God has made us free in Jesus Christ. Unlike other religions, we do not labor under a heavy burden of rules and regulations. We do not answer to other humans, but to God.
Nevertheless, despite the fact that we have freedom, we sometimes need to behave like slaves. This is in following with the example of Jesus Christ (Phillippians 2:5-8). We often need to show our love for others by relinquishing some of our freedoms instead of bickering with others. We need to be sensitive to the expectations of other cultures in order to reach them with the gospel:
For though I am free from all men, I have made myself a slave to all, so that I may win more. (I Corinthians 9:19 NIV)
In this context, it is a good thing to make ourselves slaves to others. All that Paul means here is that he is willing to abide to a degree by other peoples expectations in order to not be insensitive. Below are some practical examples of how we can do this.
ALCOHOL. I believe that the Bible teaches clearly that Christians are allowed to drink as long as they do not get drunk. But we should not use this liberty to offend others. If we know that someone is bothering by our drinking, we should not do it around them.
HEAD COVERINGS. There are many cultures that believe that women should have their faces veiled much of the time. Christian women who live in these parts of the world should follow the local customs as regards head coverings so as not to offend others or appear to be flaunting their sexuality.
MUSIC. Christians should be careful not to embarrass others by playing heavy rock music around those who might be bothered by it.