What is meant by "communicative language teaching"
In more conservative approaches grammar plays a primary role and communication is often merely a pretext for grammar analysis. In CLT grammar plays a secondary role, supporting the primary goal of communication. The psychological basis for this approach is rooted in the cognitive theory that you must acquire systematic knowledge of a language in order to use it spontaneously and that such knowledege must be acquired through application, not learned by abstract analysis.
Here are a couple of links about communicative language teaching:
I'm not a teacher, so please consider any advice I give in that context.