Human interactive that emphasizes physical closeness and emotional openness. The phrase is often used disparagingly in contexts where hard and businesslike behaviour is the norm.
The allusion is, of course, to the demonstration of one's empathy for another by touching or hugging them.
This term originated in the USA in the 1970s; for example, this piece by Nicholas Von Hoffman from The Charleston Gazette, March 1972:
"He [Walter Mondale] has something of the high school teacher in his manner not that he's stiff but he doesn't do that touchy-feely-stand-close kind of thing that marks an American politician when he's trying to do something special for you."