'Matching' is the process of comparing your order to all the other current orders which want to do the opposite to you, and finding anyone you can deal with.
You may 'match' immediately when you put in your order, which is what will happen if someone is already on the order board, and wants to deal at your terms, or you may match later if no-one wants to deal immediately but someone turns up later.
Also you are quite likely to part-match sometimes. This means that one or other side has only been able to execute a fraction of the business they wanted to undertake.