This trainer exists because you're busy but determined to shape up nonetheless. The good news: You can accomplish amazing things by training four days per week!
Those other three days are still important, though. In fact, how you can handle them can mean the difference between success and failure.
At least one of these three days should include very little activity - really try to chill. But on two of the rest days, do what's called "active rest." I suggest adding cardiovascular work to increase your heart rate and metabolic rate.
Active rest helps both your body and mind. Soreness is natural after the workouts, but the rush of exercise makes you feel better mentally.
You won't whine about how sore you are if you actively revive your muscles and your mind. Exercise crushes stress, and stress disrupts sleep and can increase cortisol levels. No bueno.
This light activity shouldn't be intense. It can be as simple as climbing the stairs to your office instead of taking the elevator. Take a leisurely stroll in the park with a loved one. Ride your bike at a leisurely pace. Sex is an awesome option for cardio - try it sometime!
The point isn't to exert yourself on these active rest days, it's to get you moving, burning a few calories, and stretching the muscles you worked so hard earlier in the week.
More experienced weightlifters will need less rest than beginners, just because they have stronger, higher-endurance muscles. The older you are, the most rest you'll probably need. Massages can also help speed recovery (via increased circulation and reduced swelling/fatigue).
Rest is important. In the gym, you break muscle tissues down. Later, your body builds muscle when you rest and while you sleep, so take the time to recover. Your body will thank you!