The underlying purpose in the development of contemporary worship was a desire to express devotion to God in ways that resonated with contemporary cultural markers in a unique context. One of the most influential places for this development was in Southern California, and John Wimber's Vineyard congregation can serve as a primary source. Wimber had been a professional musician and worked, wrote and arranged for the Righteous Brothers. When listening to his congregations original music, and looking at their worship practices, it is easy to see how their laid back beach culture highly influenced how they "did" church.
When asking the question "What is your contemporary?", we can get dangerously close to the idea that individuals should design their own worship to fit each particular need. One of the characteristics of contemporary worship that has issues with the communal economy of God as Father, Son and Spirit is the practice of encouraging people to "do whatever you need to get in a state of worship". This makes worship a pragmatic event, that fits the needs of the individual.
Instead, when we ask this question, it should be "What are the elements of our particular culture than can greater inform how we can interact with God in a corporate state?". That makes the question longer and harder, but it makes us think about the environment that we are in and we minister to? Is it appropriate to have an older worship band with multiple vocalists when the congregation and community around it is young and dis-engaged? Is it good to have a younger male worship leader with rock star clothes leading in a community of with a high grouping of lower income single mothers? This question causes us to grow, to find holes in our communities theological headspace, as well as look at how our worship does or doesn't make sense to non-Christians in our midst.
This doesn't mean that we pragmatically design worship either (making changes for the sake of a certain goal), but that we are careful to see what and who our culture is. Worship is the event in which the church works out what she believes, and she believes what she worships. It matters deeply, and to plan worship by filling in holes we miss seeing where our congregations need to grow theologically and the type of God we proclaim in our worship. These questions aren't about just music, but the way that we present the story and world of God to people, and how we as Christians interact within it.
So, with all that said, What is your contemporary?