The common thought surrounding this is that variety of exercise keeps one from becoming bored. True enough, for many, but there are physiological reasons behind the theory as well. These physiological factors are absolutely essential to know for anyone who trains for a sport.
When you do one activity, your body gets good at it. So for example, if you run 10 miles everyday, your body will improve at it, and you won't reap the same benefits on day 30 that you did on day one. You may think that it's because you are in better condition, but that is only part of it. Your body's neuromuscular coordination for that activity improves and you begin to do it more efficiently. These learned movements are called engrams. You get better and more efficient, so the same amount of exercise gives you less and less benefit.
The second physiological factor is that the energy system that you are stressing starts to plateau. If, for example, you bench-press every other day and you always do 10 reps, than you are training your ATP/CP system. The same as with the run, the stress load on the system alters, and your body starts to peak, then it plateaus. Once it hits a plateau, you need to change what you are doing or you will stop making gains, in fact, if you continue to do the same routine, you may overtrain and even lose fitness.
Don't worry if you don't understand all of this. We are looking at the big picture here and, at this point, we are only interested in generalities.
The trick when exercising is to keep your body making gains. To do this, you will need to alter what you are doing whenever you start to plateau. When you are exercising regularly, one energy system will plateau somewhere between four and seven weeks. That means you should alter your workout about once every four to seven weeks.
To better understand what I am saying, let's take an example of a runner training for a race (a coached runner, I should add). Pre-season, many months away from the time of the big race, the runner may put in a lot of easy mileage. This is their foundation phase, where they build a proper base to work upon. This may be followed by an intense period of interval training geared toward building muscle. This is a hypertrophy (or muscle-building) phase, where you add needed muscle. As the season starts, the runner may train through early season races, meaning that they won't try and peak for the race but train right up to it and treat a race as another workout. You are now training specifically, but too intensely to peak. This is the runner's power-endurance phase. As the race approaches, they will need more rest so the training becomes specific and pointed toward the big race. Training is intense but more time to recover between workouts is given. This is a power phase. As the race approaches, the runner must peak so they cut back on their training, doing only maintenance and skill work, while allowing their body's micro-trauma to recover so that they are 100% for the big event. This is a rest phase which is geared toward peaking.
This might seem obvious because they have a race to run but the principles involved are exactly the same for a 50-year-old trying to shed a few pounds. Your body responds the same, whether you are a couch potato or an ultramarathoner. Now knowing this, why would you want to train any differently? You wouldn't, and you shouldn't - you should train in phases.