The Office of Intelligence (also known as the Office of Intelligence and Counterintelligence) is an intelligence agency within the United States Department of Energy. The United States has many different intelligence agencies, and the Department of Energy's Office of Intelligence is a small, specific and very important one.
The major role of the Office of Intelligence is to analyze scientific, technical data relating to energy related issues, which for the most part means nuclear weapons, and the possible proliferation thereof. Presumably, the intelligence mostly comes from other sources (such as the Central Intelligence Agency) and is only analyzed by the Office of Intelligence. However, the Office of Intelligence, like any intelligence agency, does not go about describing their methods on their webpage.
Sources on the Office of Intelligence are not exactly clear as to what they do and how they do it, other than the obvious tracking of nuclear weapons or radiological waste. The Federal Budget doesn't specifically lay out their structure or expenditures, only noting that 1.2 billion dollars of the Department of Energy's budget go to "Other Defense Activities", which is a small sum of money, by national security standards. (Although I doubt this number is totally accurate.) It is also not clear whether the office currently is in charge of counterintelligence as well: The Main DOE webpage doesn't mention it, but a page associated with the Hanford site does, as well as offering a helpful movie entitled "You are a potential recruit".
That the United States has an agency dedicated solely to scientifically investigating the dangers of nuclear weapons and nuclear waste is not a surprise, and the fact that it is hard to find out the details of what this agency does is not a surprise either.