It means you have opened a position by buying or selling something in the market and the trade is still in progress. It becomes a closed trade once you sell what you have bought, or cover what you sold. This is elementary stuff so suggest you do the babypips school as a start and have a read of this thread http://www.trade2win.com/boards/first-steps/89078-essentials-first-steps.html
its not the only meaning, in banking open trades can also refer to trades which have been executed but not yet settled (trade date v settlment date) e.g. the cash or the security (or both) has not transferred yet.