Let's assume you have four cooks. In SOA, you assume they hate each other, so you strive to let them have to talk to each other as little as possible.
How do you do that? Well, you will first define the roles and interface -- cook 1 will make salad, cook 2 will make soup, cook 3 will make the steak, etc.. Then you will place the dishes well organised on the table (so these are the interfaces) and say, "Everybody please place your creation into your assigned dishes. Don't care about anybody else.".
This way, the four cooks have to talk to each other as little as possible, which is very good in software development -- not necessarily because they hate each other, but for other reasons like physical location, efficiency in making decisions etc.
It also means you can recombine the dishes (services) as you like. For example, you might just use the dessert to service a cafe, or just take the soup and combine it with a bread you bought from another company to provide a cheaper menu, or let other restaurants use your salads to combine with their dishes, etc.
One of the most successful implementation of SOA was at Amazon. Because of their design, they could re-package their whole infrastructure and sell it as Amazon Web Service.
*This is only one aspect of SOA.
