The physical benefits of strength training are frequently discussed: increased muscle mass, being more useful, reduced injury, fat loss, being more attractive, and increased longevity in life. What is less frequently discussed are the mental and emotional benefits.
People start strength training to get stronger. This is obvious, but what most find is that they become mentally stronger. It puts your problems in perspective; if you can grind through a heavy set of squats for five sets, going to that meeting tomorrow with a vice president of the company might not seem as daunting. After grinding through and forcing yourself to be uncomfortable again and again and again, you'll find that life becomes more comfortable. Obstacles that once seemed impossible are now manageable.
Personal Responsibility and Pride
Strength training gives you a sense of personal responsibility that extends into all aspects of your life. You can't blame anyone for your failures in the weight room, and you'll start to look at your failures in life this way. It turns thoughts from "it was their fault this happened to me" to "how can I fix this to make sure I don't fail again?" This is the only way it works in the weight room, so you start to think about fixing the problems instead of looking for a scapegoat in your entire life. Training also makes you more confident. Having the confidence to look at 315lb on the bar and squat it for a set of five will give you the confidence to do other challenges that you wouldn't otherwise have tried.
Achieving training goals in their own right deserve a sense of pride. When most people start, they can't imagine lifting what the strong guys at the gym lift, but many months or years later, they too are squatting 405. This is especially true of women. Women can be intimidated by the weights lifted by their testosterone infused counterparts, but after a year or so, they will see that they are lifting more than some of the guys in the gym which is a massive point of pride.
Putting Your Problems On Hold
You just got done working your job (be it your dream job or a shit job you just do to get a paycheck), and you screwed something up. Your boss chewed you out or a client was disappointed. You're bummed. At the same time, your significant other is mad at you from something that happened this morning. To top it off, someone you thought you could trust let you down. These days happen, but at soon as you walk into the gym, you can forget about all of that.
The only conflict in your mind now is the bar and its weight trying to use gravity to crush you into the earth, and you overcome. The bar never lies, never lets you down, and never changes. For an hour or two, you can forget about all your problems and just lift. It's a great escape, and you can finish a successful session, brain brimming with endorphins, and go home more relaxed and happy.