Very few people who workout and train will take proper rest between sets. Attempting to rush through a workout can save you time. This could even be seen as unproblematic if you get the proper rest you need after your workout is done, plus proper sleep and nutrition. However, you may be able to improve your overall fitness and the effectiveness of your workout by taking proper rest between sets or exercises.
Your body reacts to the training you do in terms of maximal survival. Your body doesn't know that you're marathon training; you could just as well be stalking an animal for miles because it's the only nearby source of food. Accordingly, your body will get better at storing fat to account for potentially long periods without food. The same works for weight training; you could be bench pressing a heavy weight or pushing a dangerous animal away from your face. To accommodate, your chest muscles get stronger in case that happens again.
Therefore; if you don't rest properly between sets, your heart will stay in a state of unrest in anticipation for the next task. You want to train your hear to reach its natural resting state FASTER even after strenuous training, which is the sign of an elite, healthy heart.
So how do you know when you are taking adequate rest between sets? You should monitor your heart rate throughout your training to find out. There are wrist HRM's that you can generally buy at local department stores or online. Use one to record your resting heart rate. Then perform a set of an exercise, and do not perform the next set until your heart has reached its resting state.
This may initially feel weird, because you could be waiting a full 5 minutes for your heart to rest again, but the more you train in this manner the less time it will take for your heart to return to normal. This will increase your heart's ability not only to adapt to different levels of high energy training, but you body will better handle physical or mental/emotional stress from this training.