An 'order' is an attempt to trade gold on terms you dictate. You state the quantity, your limit price, which vault etc.
Your order will be compared against other customers' orders. If you want to buy, and they want to sell, and your limit prices are compatible, then your order will be executed and you will have dealt, exchanging gold and money with each other.
If no-one has posted an opposing order compatible with your order yours will probably be posted (in fact you control this by managing your order duration).
When you place your order there is a balance to be drawn between the price you're prepared to trade at and the likelihood of trading. For example, if your order is for buying and you post a low price limit, you probably won't buy, at least not immediately, but you might buy a bit later, and if you do you'll have bought at a cheaper price.
You must have the resources to settle your order for it to be accepted during validation. This means you cannot post lots of orders if you have insufficient funds or gold to settle them all, each in isolation.
It is unlikely that both parties want to trade the same amount - and this means orders very commonly execute in part, and therefore take a number of executions to be filled up.
A new order will deal inside its limit if it can, meaning that if you place a purchase order with a price limit at $15,000 per kg, and someone else is already advertising a sale price of $14,950 per kg, then you will pay $14,950 on what they are prepared to sell to you and they will receive that. This saves you $50 per kg. This is because a posted order (in this case the $14,950) offers a firm price.
All orders are treated in strict sequence according to the time BullionVault receives instructions. This means you might see a price and try to trade on it, but be beaten by someone else. Not until you have received your response from the system do you know whether your order executed or not. The response is formalised with a dealing advice and later a contract - both of which are sent by email.