Deep Thought is the giant, city-sized computer that works for 7.5 million years to come up with the answer to life, the universe, and everything. The answer is 42—the problem is we don't really know what the question is. It's also the computer that comes up with the idea for another, earth-sized computer (called "Earth") that will come up with the question.
Like Marvin and Eddie, and just about every computer we see in this book, Deep Thought isn't a coldly calculating machine, but a very emotional personality. When its programmers suggest that it can be compared to slower computers, Deep Thought responds with "unconcealed contempt" (25.17) and "Contemptuous lights" (25.26). And Deep Thought even shows some empathy (more than Eddie or Marvin, at least) when it notes that the new programmers aren't going to like the answer (27.41). So Deep Thought provides us with at least two jokes or surprises: it's an emotional computer, and it gives what seems like a nonsensical answer to life, the universe, and everything.
Is Adams making fun of us for running around trying to find an explanation for everything even though we don't really know what questions to ask? You decide.