There are many definitions out there, but they all point towards roughly the same thing:

* A science of well-being   
* A science of well-being and optimal functioning   
* A scientific study of the strengths and virtues that enable individuals and communities to thrive     
* Positive psychology is the study of the conditions and processes that contribute to the flourishing or optimal functioning of people, groups, and institutions     
* The scientific study of what makes life most worth living 

The rest of this article just expands on the above and adds some detail - if you already get the message, stop reading now!

Martin Seligman founded positive psychology when he became president of the APA in 2000.  His premise was that, quite understandably following the World Wars, psychology had placed a lot of focus on what is wrong with people - curing what ails them.  Perhaps too much.  The purpose of creating a field called "positive psychology" was to attempt to redress this balance.

It's not a new field.  It's just a label that pulls certain topics under an umbrella to get research going in a particular direction, and bring together lines of research that might previously have been separate.  Of course, once you start labelling something, people will identify with it and start to relate to it.  So naturally people will call themselves positive psychologists, there will be debate over what topics should fall under its purview, etc.  But really, that's not important.  These topics have been discussed within psychology as far back as William James's "Healthy Mindedness" in 1902.  The topic is not new - the labelled umbrella is.

To give a few examples, the following topic areas fall under the positive psychology umbrella, but have been studied for a long time; some for decades:

* Happiness / subjective well-being  
* Optimism  
* Emotional intelligence  
* Intrinsic motivation  

But try looking for papers on the following topics before the year 2000, and you'll find much less to go on (Gable and Haidt, 2005):

* Awe  
* Curiosity  
* Gratitude  
* Character  
* Strengths  

That's basically the gist of it.

Isn't this prescriptive?

Although, naturally, there are applied ends in mind with the discussion of many of these topics, and some people feel positive psychology is a little prescriptive (Seligman even said one aim of pos psych is to increase the total tonnage of happiness in the world).  

I'm not sure I completely agree with that.  I don't read papers saying "People should do xyz", just the usual "We found that x resulted in y."  If the problem is the study of topics which might become prescriptive in applied settings, the same argument applies to clinical psychology, and pretty much every other science too.  Having said that, I do roll my eyes when yet another positive psychologist publishes a self-help book (how many books on happiness to we really need???).

Why not get rid of the bad, then work on the good?

There's an argument that can be made.  Why, if there is so much suffering in the world, do we not get rid of that and then all get to work on the positive side of things?

It's a good question.  But maybe the study of removing suffering isn't enough.  You could argue that by studying the negative aspects of life, you are creating a lexicon, adding words to common vernacular... perhaps this alone isn't beneficial.  Perhaps you can't get rid of the bad solely by studying the bad.

Also, I'd question why 'removal of suffering' is zero point in this argument.  The common way to describe this (which might not be all that accurate, but makes the point), is the -10 to +10 scale.  If you go for psychotherapy, it's to remove your illness.  So you go from, say, -6 to 0.  But why zero?  Who decided that one? Why isn't the 'zero' point +3; maybe a low level of contentedness? (or, why isn't removal of suffering -3; however you want to look at it).  That's an inherent principle of positive psychology - 'good' is not 'absence of bad'.

What positive psychology is not

The number of things that positive psychology is not is essentially infinite, so to save space I'll mention just a couple of things off the top of my head:

   * The alternative to 'negative' psychology  

Calling a movement "positive" psychology and saying there has been too much focus on disorder up to a certain point is not the same as saying that there is "positive" and "negative" psychology.  For most things that are studied, you probably couldn't apply either label and be happy with it.  Certainly clinical psychology you could say had gotten skewed, which I think is probably where the reaction of positive psychology largely came from, but no one is claiming that everything that isn't "positive" psychology is "negative" psychology.

Also, the claim is not being made that 'positive' topics are better in some way, or can teach us more about people and the world.  Or that 'negative' topics are worth less or can teach us less.  On the contrary - you could claim that it is precisely because the study of disorder has proceeded at such a magnificent rate that an imbalance between this and 'positive' topics has become apparent!! (Gable&Haidt, 2005)

   * Positive thinking  

Sometimes, I wish positive psychology had been called something else.  I'll be honest, I find the name quite cheesy, and I cringe inside a little every time someone asks what I'm studying.  They assume I'm talking about positive thinking, Tony Robbins, or the "Law" of attraction.  

It is not a prescription to only look on the bright side.  Instead, it's a call to study these things scientifically.  If all the data points to positive thinking, so be it; if it doesn't, that's fine too. 

It is also not a denial about problematic mental states, which are real and debilitating.  This is not a take-over!!  The study of topics like well-being, character, gratitude etc., is supposed to go alongside other topics - not take the place of them!

References

Gable, S.&Haidt, J (2005). What (and Why) is Positive Psychology? Review of General Psychology, 9(2), 103–110

See this paper also for more info:

Seligman, M. E. P.&Csikszenmihalyi, M. (2000). Positive psychology: An introduction. American Psychologist, 55, 5-14.