In a nutshell, Watson is an impressive demonstration of the current state of the art in artificial intelligence: a computer's ability to answer questions posed in natural language (text or speech) correctly.
Watson came out of the IBM DeepQA Project and is an application of DeepQA tuned specifically to Jeopardy (a US TV trivia game show). The "QA" in DeepQA stands for Question Answering, which means the computer can answer your questions, spoken in a human language (starting with English). The "Deep" in DeepQA means the computer is able to analyze deeply enough to handle natural language text and speech successfully. Because natural language is unstructured, deep analysis is required to interpret it correctly.
It demonstrates (in a popular format) a computer's capability to interface with us using natural language, to "understand" and answer questions correctly by quickly searching a vast sea of data and correctly picking out the vital facts that answer the question.
Watson is thousands of algorithms running on thousands of cores using terabytes of memory, driving teraflops of CPU operations to deliver an answer to a natural language question in less than five seconds. It is an exciting feat of technology, and it's just a taste of what's to come.
IBM's goal for the DeepQA Project is to drive automatic Question Answering technology to a point where it clearly and consistently rivals the best human performance."