This is a very interesting verse. It has specific application with regard to what was happening in the church of the first century, and it has a principle application in the church of the twenty-first century. First, let's talk about the application to the church at Colossae. The Colossian heresy was basically a group of additions to the teachings of Christ. It was used for either zeal for or skill in any art or science or branch of knowledge.
Philosophy refers to any moral system.
Here in Colossians the specific philosophy Paul warns against is the idea that one must believe in and practice certain aspects of the Law of Moses, along with secret knowledge supplied by false teachers and traditions of men, along with the Gospel of Christ. In other words, this philosophy will not help you to live for Christ, in fact it will hinder you. It will take you captive. The apostle Paul faced a similar situation in Athens. Now while Paul was waiting for them at Athens, his spirit was being provoked within him as he was beholding the city full of idols.