Hi Gizmo,
Nicolette is correct that it is based on eastern practices. Psychology has adopted some of these concepts and adapted them to help those who have to deal with intense or painful emotions or life situations. I am not someone who is into alternative therapies or interested in Buddhism at all but through working on my eating disorder have come across these concepts in the way they are used in psychology.
They are concepts that are linked to DBT and created by Martha Linahan who developed a programme for treatment of those with BPD. But DBT is being used more and more for those who have problems with emotions such as those who self harm, having addictions or eating disorders and those with trauma.
DBT is based on a CBT approach and emphasises an acceptance of the person as he/she is, combined with the expectation that current behaviours need to change. The tension that arises between this need for both acceptance and change is known as a 'dialectical tension'. Dialectics is the practice of finding the middle ground between two opposites (Linehan, 1993a).2006
So really it is about simultaneously managing both acceptance of painful emotions and situations whilst then working on changing what needs to change and developing skills to do so.
Some CBT has now adopted some of the techniques used in DBT and so in the UK we now have what is known as "Mindfulness based CBT".
Read a bit more on
http://www.dbtselfhelp.com/html/radical_acceptance_part_1.html for more information.
These exerts don't really give you the information you need though. I have not been lucky enough to have face to face treatment as in the UK as it is still almost solely used for treating BPD (unlike the states and Australia for example) but have read books and asked questions. I tried hard to face to face DBT but no joy. :( I would recommend a book called, "Don't Let Your Emotions Run Your Life: How Dialetical Behavior Therapy Can Put You in Control by Scott E. Spradlin. I don't do the meditions but do use the concept a lot and it has helped me very, very much in my life.
Radical acceptance is about taking something that we maybe really don't like at all and totally accepting that it is what it is. That can be used in many situations. It can be used when looking at things that happened in the past; emotions; looking at who people are; things we have done etc. In western cultures we tend to teach fighting against so called "bad" emotions and the problem is that the more we fight the worse we feel. It increases the intensity rather than decreasing it. So by accepting things we let go of them and that in itself causes much more change than all the fighting does.
These concepts are particularly helpful for all of those of us who have had invalidating childhoods which I suspect is almost all of us with unhelpful pasts. An invalidating environment is where children are not taught to listen and express their emotions and their emotions or self expression is either rejected, discouraged or cruelly punished. That cause all sorts of problems.
Feel free to ask me questions Gizmo's! I hope I haven't been to confusing.