Please note that this is an outdated version of this article. You can find the updated article here.
Orders remain open if they have not yet been fulfilled. When you set a buy order for a certain quantity of an asset at a certain price, there have to be sellers available who are able and willing to sell to you at that price and quantity. If there are not enough coins for sale at that price, the order remains open until there are enough sell orders at that price to fill your entire buy order.
The same is true for sell orders, which remain open until there are sufficient buy orders at the correct price to fulfill the entire sell order.
Please be advised that these orders will remain open until the parameters that you have set have been met in order for the full order to be completed.
You can review all of your current open orders here: https://poloniex.com/openOrders