Per the Wikipedia: Groupthink is a psychological phenomenon that occurs within groups of people. Group members try to minimize conflict and reach a consensus decision without critical evaluation of alternative ideas or viewpoints.
When we covered this in psychology class in college, the example they pulled was the failed Bay of Pigs Invasion. Basically, a bunch of thinkers in Washington, locked in a room together, came up with a plan to train former Cubans with CIA tactics, land them in Cuba and have them take over the Cuban government.
On the face of it (and with 50 years of distance) it's not a horrible idea on its face: Cubans attacking Cuba is not a declaration of War by say, America, but, if successful, achieves America's aims--the primary one was to provide Fidel Castro a dirt nap.
As of the time of this writing, Fidel's still alive and his brother is running the show, so you can guess that the invasion was not nearly as kick ass and effective as the people plotting in a room in DC thought it would be for folks on the ground in Cuba who may not have set foot in the jungles of their native land, ever, and who probably hadn't been back for five or more years. People who probably couldn't find their local supermarket anymore, chosen entirely on the fact that they were Cuban (and not say, on their prowess with the weapons and skills they'd need to take over the government) might not be the most effective take over force...but, the problem was, the guys in the room had Group Think.
In Group Think, members of a team become so familiar with each other and their methods of thinking and working that they sometimes miss very important things such as "lack of early realization of the impossibility of success by covert means, inadequate aircraft, limitations of armaments, pilots and air attacks to attempt plausible deniability, and ultimately, loss of important ships and lack of ammunition" which were determined by a Board of Inquiry commissioned by President Kennedy, who, incidentally, was one of those guys in the room in DC.
When Group Think happens, the team is actually working together very passionately and very strongly. It can seem extremely productive...until suddenly its not. Clues that your team may be having Group Think behaviors are pretty simple: people stop disagreeing with each other. Not necessarily entirely (though that is a major warning sign), but on major components of a plan. Which is not to say that your team should be in constant turmoil arguing with one another, but they should be questioning everything, and doing things that let you (and other members of the team) know that they are looking at all possibilities. For example, you may pick a specific architecture of a piece of software, but if all your devs do is just implement what was picked and don't have anything to say about the future "what ifs" of the project, that's a warning sign.
When I was working with a team that was in Seattle and in Boston (the client's team was in Boston and my consulting team in Seattle), we fell into Group Think briefly; it was understandable. On a project you assume everyone is pulling in the same direction or at least trying to find the best direction in which to pull. What was happening, though, was that we were meeting our obligations and still, regularly, getting in trouble with our client.
Investigation determined that the Seattle team was in Group Think about the direction the project should go, and had not counted on the independent contractors in the Boston team, so they had not been looking for what that team was doing. They were so convinced that the Boston team would be complimenting and adding to their work, that it was several weeks of chasing our tails before we eventually realized the Boston team was--inadvertently--actively working against us. It was inconceivable for us as a team that another team could be working counter to what we were doing, especially when they were attending meetings and saying all the right things. But that's what was happening, because it turns out the client hadn't really wanted to hire us, and he wanted to manage the whole thing himself. So he was being subversive and since it was outside the conceivable paradigm for our team--despite the mounting evidence--Group Think blinded us to fixing the problem.
It almost cost us an on time completion, but once we accepted the facts right in front of us, we were able to counter the counterproductive work and, though it was the longest Death March project I've ever run, we came in on time and on budget. I had to bring toys and games and books to work, and the team would get one randomly chosen from a bag each time they countered the work done by the Boston team that was aggressively fighting the direction we were going on the project. Morale stabilized with free Starbucks cards and Far Side books. But it was a long slog, and it could have been even longer if we hadn't managed to break the Seattle team out of Group Think on the project.
From a management perspective, you're probably wondering what I was smoking to allow this to happen, and that's really another story for another time. Sufficing to say I wasn't sitting on my hands during this experience, but that sometimes, things that are bad happen, and you have to roll with them. Fortunately, Group Think is not one of those things.