Service Oriented Architecture - A set of conventions and standards that permit functionality, such as web services to be found, and remotely invoked over an internet or the Internet.
Early in SOA's history it was usually used to describe the supporting technology needed to make component functionality available in a remote, shared environment. At that time, it had come to be known specifically, as a set of technologies for allowing remote access to shared functions by way of an XML protocol called SOAP.
As stated, the above description was culled from early SOA development. Those promoting and discussing SOA today usually either don't define it at all, or define it only in terms of the benefits it promises to deliver to adopters. The book "SOA for dummies", for example, presents multiple bullet lists of promised benefits, each billed as a definition of SOA, without ever actually defining SOA. Here's a definition (and example) from the Internet:
SOA is an architectural style whose goal is to achieve loose coupling among interacting software agents. A service is a unit of work done by a service provider to achieve desired end results for a service consumer. Both provider and consumer are roles played by software agents on behalf of their owners.
This is actually one of the better ones. Early in SOA's history REST was considered an alternative to SOA, now it is embodied within most SOA "definitions". The above definition is a good example of this.