A limit order is an order placed to wait and buy or sell only at a specific price, and it will sit there until a market order comes through that satisfies it.
A market order is an order to buy or sell at whatever price is acceptable right now, as per the available limit orders.
The set of unsatisfied limit orders at any given time is the "order book".
When an order occurs within an exchange, it has two sides; a market order which initiates one or more transactions, and one or more limit orders that are consumed to satisfy the whole of the market order.
Let's say that the current order book shows 25BTC available to buy @ $99.00, then 20BTC @ $99.10, then 130 @ $99.20, then 50 @ $99.30. This means the current buy price is $99.00 because I can buy bitcoins right now at $99.00. Now let's say I want to place a market order to buy 100BTC right now. To satisfy this order, I first buy up the 25 BTC inventory available at the $99.00 price point. Now that there are none left at that price, I need to buy at the next price point, $99.10. So far I've bought 45BTC of my 100BTC order. Now the cheapest remaining BTC in the order book are the 130BTC at the $99.20 price point, so I buy 55BTC of that, thus completing my market order, and leaving 75BTC still in the order book at the $99.20 price point. Given that that is now the cheapest available price for BTC in the order book, we can say that the price just changed from $99.00 to $99.20, hence the price moved up, as you would see at a glance.
Similarly, if I place a market order to sell, then I am consuming limit orders on the buy side, starting with those paying the highest rate, then the next highest rate and so on until my sell order is satisfied (i.e. my BTC are bought by the buyers who placed the limit orders to buy). Because I'm consuming limit orders that pay the highest price first, then they will no longer exist when I am done, and the next highest will be the best remaining price that anyone is willing to pay, so it can be said that I am driving the price downwards.
You will note of course that both of these (market orders to both buy and sell) can consume the available limit orders in both directions at the same time. That's where the "spread" comes in. It's the area between the highest "buy" price and the lowest "sell" price. If market orders are executed that consume all of the limit orders around a given price point, the spread grows. What happens next is that people who want to be the first to be chosen to be bought from or sold to then go and place new limit orders inside the spread area, thus closing the gap between the highest buy price and the lowest sell price. A healthy market generally has a low spread, as people exist who both want to buy and sell. If the market is falling, the spread will tend to be filled only with limit orders to sell, which pushes the spread area down towards lower price points. When the market is rising, the opposite happens.
This is great, well done.