That's a great ? MO, and one I've thought about off and on now for the past hour. The most honest answer I can give is that it varies wildly, depending on the situation. When I take one of my children hunting, it's always been, just give me one of those "WOW, dad, that was so _____ (insert one of many good adjectives) when..." moments. When helping clients, it's really all about what makes them happy. That may sound cheesy, but isn't making clients happy what's important to any business? Sure, money is as well, but if clients aren't happy the money eventually stops. some are all about the kill and sooooo grateful when I put them on a buck they want and they kill it. You'd swear you just did something on the level of saving one of their loved one's lives, when all you did was get lucky enough for your intel to lead you the right way and the buck to cooperate. Other times they are happy just to see more deer than they did before they hired me, and the rest is just a bonus.
For my own hunting, it also varies wildly, depending on the situation. seeing a buck I was worried was dead can be a huge success. The days I've arrowed 3-5 does in a single sit (on disgustingly overpopulated grounds), finding them all was a big success. When hunting with friends, getting them to come back all shaky is a success no matter what I did. I kind of hate to admit it, but there are also times on the other end of the spectrum that if I don't kill the buck I'm after that sit, it takes something else pretty darn special happening to consider the sit a success. That's not a good thing, but it's an honest answer.
How I kill deer even plays into this. Last season I killed a 6.5 yr old buck that I'd tracked for 3 seasons. He was the first really good buck I'd actually seen on the property (both in pics and while out scouting) and, as cheesy as it sounds, was my security blanket. He wasn't overly predictable, but I could count on him being there through the horrific drought and 2 runs of EHD/BT. He gift wrapped himself for me to the point that I told my buddy he needed to hurry up and get ready, that I was killing that buck that day (I've never said something like that before).
That sit was a horrific disaster that would embarrass most first time hunters. I did everything in my power to mess it up, with one stupid thing after another, along with 2 groups of turkeys and a bobcat also doing their best to mess it up for me. I had 3 legit chances to kill him, spooking the doe he was with twice (not turning her inside out, just making her nervous enough to alter course) before finally spine shooting him, climbing down, sending an arrow through his heart at point blank range and then talking to him as he died. I couldn't consider it a "successful" hunt. I felt like an a$$hat. I had another like that, where I arrowed a buck text book quartering away (never shoot for the opposite leg. Instead, tuck it behind the last rib, through the liver, diaphragm and into 1 lung...MUCH more effective shot). I then chased him for 800ish yards, putting 2 more arrows into him before it was done. Hard to consider it a success after putting that buck through all that (his hide literally had a fine, dense, spider web of veins on it when I pulled the hide, from how hard I'd pushed him...never seen that before or since).
Extremely long way of saying, "success" to me is very situation specific. For the season, ultimately, if I can look back and say I had fun, nothing horrific happened and learned some things, it was a success.