Your question specifically refers to Tuckman's Stages of Group Development which aim to establish a patter of behavior, from the moment a leader enters a group, to when he changes it, and then brings out results from that change.
It is known that change is a very hard thing to do, especially when one has reached a comfort zone. In groups, each individual has his or her own comfort zone and, for this reason, it is imperative that whoever leads that group does it gradually and consistently. There must be much substance to the process.
Hence, a common and typical example of how groups change is when a person is put in charge of a group of people who already have a way of doing things. This is typical of just about any field. Examples include: a) A new teacher entering a classroom that used to have another lead teacher and follow her rules; b) A new supervisor or leader that needs to fix a specific department; and, c) a soldier assigned to a platoon which he or she will have to mold to best benefit the common goal.
In the latter case, the case of the soldier, this is how the dynamics often are: A platoon needs to be put together to accomplish a mission. The men in the platoon have previous knowledge of what they have to do, but they do not have any knowledge about their leader.
A- When the new leader comes in, he often enters already having established (forming) the goal, the mission, the vision, and the expected outcomes.
B-This, is often met with resistance, for which the leader must come in strong regardless of the attitude of those who need to follow (storming).
C-Once the rumble calms down, it is time to re-connect, re-visit, and regroup by establishing the new rules (norming).
D- Now he goal is clear, the plan of action is clear, the rules are clear: It is time to put them into action and execute, which would be the same as performing.
E-Finally, you the group reach their goal if their plan is executed correctly, for which they would have gone through the process of transforming , OR ending, the mission.
You can apply Tuckman to just about any example of group dynamics there is out there. The group process is often the most evident way to produce change.