The benefits of the social connections made in attending a conference?
Suppose one made connections from a conference, then what are the potential benefits of making those connections? i.e. how to make value out of them?!


For most people, new connections found through conferences at a later stage become either


Potential references
Potential collaborators
Friends or at least acquaintances 


(or, in the optimal case, a combination thereof)

For all of those, it is hard to put a numerical "value" on them, but as you progress with your academic career, you will find that it is hard to be successful in academia without a healthy set of all of the three. Without references that vouch for your scientific merit, it is hard to get any advanced academic positions. Without collaborators, it is hard to write strong papers and grant proposals. Without friends in the community, future conferences become a chore and it is very easy to lose track of where the community is heading as a whole (also, the third item quite naturally leads to the former two items).


  Also the majority of the connections would be with researchers and students, not hiring managers so I wonder if there are any value for job search after graduating 4 years from the PhD.


In academia, the notion of "hiring managers" is somewhat suspect. You can definitely meet senior professors at conferences, and those are the ones that decide whether you get a faculty position down the road. Further, never make the mistake of assuming that the "researchers and students" you connect to don't matter, and you shouldn't talk to them - the PhD students from today are the people that review your papers and grant proposals tomorrow (hence the name "peer review").