At times it seems like economics justly deserves its epithet of the "dismal science". As an undergraduate student, certain fundamental assumptions are expounded to students, often called the "neoclassical" assumptions of economics (of course these assumptions are summarily dismantled as one advances in the field). There are two relevant ones here. First, humans have rational preferences - i.e. we are able to attach values to outcomes and choose between them. Second, humans are utility maximisers (for the purpose of this discussion we can just consider utility to be happiness). In short, I can be aware that I prefer chocolate to avocados and when given a choice between the two, will pick chocolate (problems of diminishing marginal utility aside).
So how does this tie in to behavioural economics? Well, when people behave according to these assumptions, a number of seemingly intractable problems appear. Perhaps the most famous is the prisoner's dilemma:
Two criminals have been arrested for a crime, are approached separately by a prosecutor and are told they can either confess or keep quiet, with the respective outcomes indicates above. As it turns out, no matter what Prisoner B does, it is always in Prisoner A's best interest to confess, as his jail time will lower, and vice versa. This results in a somewhat bizarre outcome where both prisoners confess and end up in jail for 5 years, whereas if they had both kept quiet they would have been out in a year (in game theoretic terms, we have a Nash equilibrium without Pareto optimisation). To give a real life example - we would all benefit if every country in the world reduced carbon emissions, however for any single country the economic costs often outweigh the benefits, and as a result most countries are relatively hesitant to cut emissions, and certainly don't want to be the first.
The overarching point here is that it is often difficult to get people to cooperate in real life, because what is optimal for an individual is not necessarily optimal for a group.
Behavioural economists have tackled this problem by devising a number of ingenious games. One such game is called the public goods game, where everyone is given a certain amount of "money" which they can then choose to keep to themselves, or to contribute to a public pot. The contributed money is then multiplied by some amount and distributed equally to all the participants. The Pareto optimal outcome here (i.e. where everyone is "best off") is if everyone contributes everything to the pot. But as an individual I am obviously inclined to shirk so that I can get the benefit of the public good without having to contribute. In typical iterations of this game, people contribute a fairly large sum to start off with, and then contribute less and less as they notice that others aren't holding their weight, and eventually contributions dwindle.
To cut to the chase, using questionnaires and alterations to the mechanics of the game, the economists discovered that most people are "conditional cooperators". In other words, I will contribute to the neighbourhood watch as long as everyone else does. However, a small number of "free-riders" cause the conditional cooperators to revise their optimistic opinion of others downward and cooperation peters out. So how can this be dealt with? Punishment, or a credible threat of punishment (as no doubt many law enforcement agencies would be unsurprised to hear) is effective, and was frequently used in the game - even when costly to the punisher. Interestingly, punishment is sufficient but not necessary to ensuring cooperation. Allowing participants to communicate turned out to be nearly as effective.
This is particularly interesting because of the implications it has for real life problems. In contrast to the sterile, often heterogeneous environment of the game, the kind of groups people form in real life are often more conducive for this sort of communication/punishment/social disdain. This suggests that collective action problems aren't as intractable as many governments think, and that there is greater scope for social co-operation in the provision of public goods (things like the local neighbourhood watch, or litter reduction campaigns).
It leads to the comforting conclusion that (most) people really aren't as self-interested as economics might suggest. The majority of people will cooperate as long as they are aware that most others are just like them. This generates the kind of optimism that is critical to sustained social interaction.
I would strongly recommend reading Experiments in Economics by Ananish Chaudhuri if you find this topic somewhat interesting. It's a great introduction to the field, and perfectly accessible, even to those who think Adam Smith is a football player.
