Lets take an example.
You have written a calculator code in any language (java, c,c++ etc) which perform 4 operations add, subtract, multiply and devide. Lets say, we deploy this code on a server. Now you want to publish this code on internet so that any person in world who has connected to internet can use your code. Now webservice will come into play. As per your server, you need to follow an implementation technique to convert your code into a webservice. For example, you are using Apache axis server and you have implemented your code using jax-ws (java api for xml web services). Your code will be published as a web service on a url ( like http://www.myserver/calculator).
Now how are you going to access this web service? Now client will come into play. Lets say you have designed a website www.calculation.com. And from there you are taking 2 integer inputs and calling your webservice using http://www.myserver/calculator/add for addition,http://www.myserver/calculator/subtract for subtraction,http://www.myserver/calculator/multiply for multiplication and http://www.myserver/calculator/multiply for division.
Now you can see each of your webservices operations addidtion, subtraction,multiplication and division is working as a service and in future lets say you have a requirement to put a equation solving service on your website then you can reuse your addition, subtraction multiplication and division web services using those links to make another service. Here you go, you have achieved service oriented architecture i.e. SOA.