I came upon this question only today, but should like to offer this interpretation based on my experience:
A 'good' handshake is one that is so generic or neutral as to be unremarkable. This will differ from region to region and culture to culture. The opposite of a 'good' handshake is not a 'bad' handshake but an 'odd' handshake which can make the recipient uneasy at a primal level and make them mistrust that individual.
If exerting a reasonable amount of pressure while shaking hands is normal in your culture, then your coach while encouraging you to develop a 'good firm handshake' was probably warning you against developing a weak or limp handshake. Because 'good, firm' being the norm, 'weak/limp' might well seem odd and give a bad impression.
Here in India men shake hands with men but not usually with women. Of course women shake hands with women. Shaking hands is common but not at all mandatory: there are many non-touch forms of greeting here and younger or low-status men are not expected to initiate a handshake with older or high-status individuals. This is the cultural norm. Rejecting a socially acceptable handshake also leaves a bad impression.
I dislike shaking hands in general, but especially dislike damp hands, fleshy palms, limp handshakes and lingering handshakes. I haven't received bone-crushingly hard handshakes since my college days, when a few classmates did try to exert more pressure in 'play dominance.' That tells me adult men here are judicious with the pressure they apply. No need to go at it too hard. Whereas a firm and quick handshake is 'good' in my opinion.
I say this only to emphasise that every person reacts differently to somebody's handshake. However, a 'good' handshake is important because shaking hands leads to the formation of a strong first impression or strong repeat impressions, and you want it to be a 'good' impression.
Note that these impressions are hardly conclusive: many fraudulent persons have good firm handshakes and one of the nicest, honest and most helpful men I know actually has a limp handshake.
Again, as other answers here have already conveyed, people tend to interpret handshakes not in isolation, but in the overall context of personality, behavior, body language and the cultural situation (for example a handshake with a bereaved friend can be exceptionally long -- literally holding hands for minutes -- because human beings express sympathy and compassion through touch gestures.)
Post scriptum: if your handshake is actually very strong then "a firm handshake you have there" is possibly an example of classic British understatement,
but if the same comment were addressed to somebody with a limp handshake, it would be an example of sarcasm/irony.