"Pugilist" = boxer, basically. So he's talking about the sport of boxing.
"On the ropes" - this doesn't just refer to someone's positioning, it refers to when someone has been badly dazed or hurt by a punch or punches. They try to back away and escape the onslaught, and wind up with their backs against the ropes that define the boundaries of the ring, sometimes even leaning on them for support to keep from falling down.
"Worth his salt" - the origins are noted by Tesujin. Basically, anyone who has any moderate or above skill or expertise would be "worth his salt."
"Combination" - in the boxing context, pretty straightforward - a series of punches thrown in rapid succession, instead of single punches. Often, when thrown in combination, punches, even if blocked or defended, serve to expose gaps in the defense for subsequent punches to land more cleanly.
"Hook" - that is a punch that is thrown where the path of the punch follows a looping path, first wide and then moving towards the center, essentially coming in from the side. Given the wider arc and distance traveled, there is a lot of potential for greater power being generated as well. The punch is especially effective in getting around defense that are set up to block incoming punches that come straight in from the attacker.
To put it all together, when someone gets stunned or hurt in boxing, quite often they're unable to think clearly, and instincts take over. This includes trying to back away from the fighter, and, also, they often raise their hands up to their head to try and prevent any more blows from landing, trying to get time to regain control of their senses and recover.
So if a fighter backs into the ropes, covering his head, hard punches to the body, initially, will hurt the fighter, and often they will lower their hands to protect their torso, which would open up the defense, leaving the head open for the subsequent punches, with the hook also having the advantage of going around hands being held up in front of the head. That combination is a standard sequence for finishing/knocking out a fighter once they are hurt.