It was named after Deep Thought, a fictional computer in Douglas Adams' series, The Hitchhiker's Guide to the Galaxy. The naming of chess computers has continued in this vein with Deep Blue, Deep Fritz, Deep Junior, etc.
Deep Thought won the North American Computer Chess Championship in 1988 and the World Computer Chess Championship in the year 1989, and its rating, according to FIDE was 2551. Compare this to beginners at chess whose rating is below 1000, and chess grandmasters whose ratings range around 2500 to 2700. Modern world champions are rated around 2800.
In 1994, Deep Thought 2 won the North American Computer Chess Championship for the fifth time, with its rating estimated at around 2600. It was sponsored by IBM. Some engineers who designed Deep Thought also worked in the design of Deep Thought 2. Its algorithms were quite simple evaluation functions, but it could examine half a billion chess positions per move in tournament games, which is sufficient to reach depth of 10 or 11 moves ahead in complex positions. Despite that, using the technique of singular extensions it could also follow lines of forced moves that reach even further, which is how it once found a checkmate in 37 moves.