The OP is asking two questions here. The title is “what do soft hands mean to you?” This is a huge question that is philosophical and theoretical as well as technical, and involves thinking about how you can ride on clear contact, for instance in collected moves, yet remain kind, giving, responsive and not “hard.” Soft does not equal light contact. It’s about how well the hands move with the horse, and how well they give or release after an aid. Release does not have to mean a noticeably slack rein.
But the actual post asks a different question, a purely technical one: how do I follow the horse’s mouth at the canter with consistent contact?
The OP says that coach wants OP to ride with softer hands at the canter. The OP can now follow the canter forward/down, but can’t retain contact on the upward/back phase of the canter. OP’s hands/arms don’t come back; the rein loops.
First, I’d want to know how long OP has been trying to do this. If this is a question after the first or second lesson on this, then it might just take a few more tries to change muscle memory. If however this problem has been persisting for a month despite repeated instruction, then here are some other things to think about.
Does the OP have excellent following contact at the walk, and perfectly stable hands at the posting trot? Do the OP’s hands bob up and down when posting, or can the hands hover motionless and independent of the body?
What is the OP’s seat like at the canter? Can OP sit the canter? If you watch FEI jumpers on TV, obviously they can maintain the exact same contact if they are cantering two point, or if they are sitting deep in the saddle between jumps. Their hands are independent of their seat. But many intermediate ammie hunter/jumper riders don’t learn to sit the canter correctly, which means that they aren’t really two-pointing correctly either. Instead, they ride standing in the stirrups, braced, flopping around with their bum slamming into the saddle. And this can cause them to tilt forward. You can’t have independent hands if you don’t have a secure seat. And you can’t follow the upward/back motion of the canter if you are tipping forward.
The OP has learned to “give” with the forward/down motion, which is good. But the fact OP mentions this suggests that up to now, the OP wasn’t allowing any forward/down, so was perhaps really leaning on the reins for support, or choking in the horse out of fear of going too fast. Both of these problems are about more than just hands.
And example of a problem being really just about hands, would be if you had some rough and ready kid with great balance and nerves of steel, who had grown up riding rank horses, and resorted to reefing on the mouth because that was all the horses had been taught. You might be able to put this kid on a better trained horse and play with how quiet an aid the horse would respond to.
But I think in most cases, problems that show up as hands are often about larger questions of overall balance and seat.
OP might try some longeline lessons, to see what it’s like to ride with no reins. Try to sit the canter, try no stirrups. Then try arm exercises, “superman” arms, hands above head, etc., to see if you can separate your hands from your seat and body. You might also try exaggerated pumping of arms in rein position, with no reins.