I'm by no means an expert on detachment. But for me it means not being so 'attached' to a particular outcome - ie: reconciling. Being more detached means being prepared to gracefully accept whatever the outcome may be. It means realising that you are not dependent on your partner for your future happiness - and that you will ultimately be happy whatever the outcome - although it may take a little while for that to be the case.
To feel your own happiness is completely dependent on your partner is co-dependency - not a good recipe for future happiness.
Detachment for me also means being a little more removed from the emotional drama of the situation. ie: not getting swept in and up and down depending on what is happening with your partner. But being a little more emotionally removed, centred, balanced and focused yourself. Choosing how you respond instead of getting all swept up and reacting.
I think it really takes ongoing work to detach and it isn't easy. I feel I manage to 'appear' quite detached. And sometimes I feel more 'detached.' But other times I don't do so well.
I also think it is the difference between 'needing' someone and 'wanting' to be with them..
Hope this helps :-)
T 13 M 7 Me 48 H 46 SS 15 BD 7.14 PA D final 5.16 (H filed)
We receive & we lose, and must try to achieve gratitude & embrace with whole hearts whatever of life that remains after the losses - Dubus