As a strength and conditioning coach, knowing "the who" is very important when working with athletes. What I mean by that is knowing exactly WHO you are working with ... what sport do they play, what is their training background, what are their goals, what makes them tick, etc. etc. Knowing and understanding each athlete's needs, both physically and emotionally, will help you be the best coach to them.
Now, I understand that this is hard to do when working with a large group of athletes (trust me, I know from experience), but you can always start with the basics. The first thing I do before I begin to program for an athlete or a team is understanding what they need for their specific sport - energy systems used, common injuries, strengths, weaknesses, etc. It's also important to know the coach's and team's goals. If their goal is to win a National Championship, then you better be sure you're going to prepare them to play that long. After looking at the physical needs of the sport and team goals, I look at team personnel. What is the training age (number of years the athlete has been training for) of each athlete and what are their movement patterns like? Knowing their training age helps prepare you by making progressions or regressions to different exercises. Using the squat for example, there may be some athletes that feel comfortable doing a barbell front squat, but there may be others that need to do a goblet squat variation with their heels elevated.
Now, I am no expert - I am simply just sharing what I personally do before I program for a team. As much as it is important to focus on the physical aspect of the training, I briefly mentioned above the mental or emotional aspect as well. I feel that this is very important to think about for some athletes. It doesn't matter how good of a program who've made, if you can't coach/instruct/motivate/ facilitate it properly, it's not going to work. Do your athletes want to get FIRED UP before every lift? Or do they want to just come in and get their sh*t done? Do they productively socialize between sets, or do they distract one another? This is where the COACH part of our title comes in handy, knowing how to deal with the athletes that come into the weight room.
I really think the best part of being a coach is establishing the relationships you have with athletes. Becoming another trusted resource for them is very rewarding and not something I take for granted. To show my appreciation to my athletes, I am going to come up with a program for them specifically, not something I just threw together - I want them to know that I had them in mind when I was determining what would go into each training session.
Knowing "the who" is essentially your needs analysis, I just wanted to ramble on about why I think it's so important and what goes through my head when I go to program. Remember, I told you all I'd give you a peak inside my head as a strength and conditioning coach, so this is part of it :)