This is such an interesting question! Group dynamics are quite complex, and as you have noticed, there are positive and negative aspects to them.
Let's start with the positive. Group dynamics can allow a group to be far more productive than any one individual. This happens when a group explores the strengths and weaknesses of its members and allows people to capitalize on their strengths. For example, if a group is expected to write a report, someone might be quite good at statistics and focus on that piece of the report. Someone else might be quite good at the mechanics of writing and be responsible for writing and proofreading the finished project. Someone else might have great organization skills and be able to allocate tasks well and keep everyone on schedule. In a group that has positive dynamics, everyone will pitch in and cooperate.
Negative dynamics create dysfunctional groups that have a difficult time accomplishing anything. In some instances, more than one person wants to be "in charge," which does not work out very well for anyone because a group should be focused on its goals, not on a power struggle. In instances in which someone is appointed as the group leader, that person's leadership style may or may not be compatible with the group's makeup or mission. A group in which the members cannot reach any concensus is not a good group. In some situtations, there is not a "getting to know you" period that would allow people to explore their strengths and use them productively. When tasks are assigned by a leader who has no idea what people are capable of, this can create resentments and poor cooperation, too. Still another negative aspect of the group is the situation in which one person does not carry his or her weight, for whatever the reason may be. Sometimes the rest of the members will work past this, but this often causes resentments, too.
Think back on any groups you have been part of. What worked well? What didn't work well? Even if you had no exposure to the theory of group dynamics, my guess is that you have a very good idea what was good and what was not so good.