To be unconventional is to act, dress, speak, or otherwise exist out of the bounds of cultural norms. If you eat cheeseburgers for breakfast, that's somewhat unconventional.
Anything that's nonconformist or out of the ordinary can be described as unconventional. Every culture has its own conventions — or norms — and what may be unconventional in one region might be typical in another. The perception of what's unconventional is determined by context.