Sorry Jezelll, had to throw a downvote. This is not what I would consider 'plain english' :( I don't have a problem with the intent of your definition, but using words like 'operation', 'remote server', 'invoked' and 'specification' makes it hard for beginners to understand. See Mitchel Sellers answer as an example of 'plain english'. – Dhaust Jun 30 '09 at 23:53
A web service is a collection of open protocols and standards used for exchanging data between applications or systems. Software applications written in various programming languages and running on various platforms can use web services to exchange data over computer networks like the Internet in a manner similar to inter-process communication on a single computer. This interoperability (e.g., between Java and Python, or Windows and Linux applications) is due to the use of open standards (XML, SOAP, HTTP).

Web services are a key component in "mashups". Mashups are when information from many websites is automatically aggregated into a new and useful service. For example, there are sites that aggregate Google Maps with information about police reports to give you a graphical representation of crime in your area. Another type of mashup would be to take real stock data provided by another site and combine it with a fake trading application to create a stock-market "game".

A web service is something that a website chooses to offer to those who wish to read, update and/or delete data from your website. You might call it a "backdoor" to your data. Instead of presenting the data as part of a webpage it is provided in a pre-determined way where some of the more popular are XML and JSON. There are several ways to communicate with a webservice, some use SOAP, others have REST'ful web services, etc.
SOAP is known as a transport-independent messaging protocol. SOAP is based on transferring XML data as SOAP Messages. Each message has something which is known as an XML document. Only the structure of the XML document follows a specific pattern, but not the content. The best part of Web services and SOAP is that its all sent via HTTP, which is the standard web protocol. 

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^ Compare: Oya 2008, "Under the current Web Services, […] stakeholder systems must follow the predefined rules for a particular business service including those about business protocols to send/receive messages and about system operation. […] More flexible mechanism is desired where freely built and autonomously running systems can exchange business messages without pre-agreed strict rules. We call it Autonomous Web Services (AWS) and proposed the framework called Dynamic Model Harmonization (DMH) with its algorithm, which dynamically adjusts different business process models between systems […]."[4]

The gaining Registrar must obtain express authorization from either the Registered Name Holder or the Administrative Contact. A transfer may only proceed if confirmation of the transfer is received by the gaining Registrar from one of these contacts. The authorization must be made via a valid Standardized Form of Authorization, which may be sent e.g. by e-mail to the e-mail addresses listed in the WHOIS. The Registered Name Holder or the Administrative Contact must confirm the transfer. The new registrar starts electronically the transfer of the domain with the help of the authentication code (auth code).

Web services use something known as SOAP (Simple Object Access Protocol) for sending the XML data between applications. The data is sent over normal HTTP. The data which is sent from the web service to the application is called a SOAP message. The SOAP message is nothing but an XML document. Since the document is written in XML, the client application calling the web service can be written in any programming language.