Help Team Member Vision
What you did in understanding principles, breaking down goals and connecting them with top principles and related goals at every level of the organization, was an example of building vision — your own vision. By using open-ended questions and examining what you wanted the group to achieve in a larger context, you established a vision of what the group's efforts meant.
Need for Personal Vision
In creating your own vision of the group's efforts, you reinforced a number of factors for your own work. One is purpose. When you don't know why you do what you do, it seems purposeless. However, when you can see a chain of connections leading from you to much larger efforts, you can more easily put energy into your efforts. Also, by putting things into context, you can proceed more reliably. You have a range of checks and balances — your understanding of the part you and your group play in a larger context. You can see if things start going off track because you see the direction in which you should be going.
For the same reasons, the members of your team also need a personal vision. It may be more restricted; depending on the structure and size of your team, people may be more involved with smaller and more focused responsibilities. But the same quality of personal vision must exist, or your fellow team members will lose a sense of relevance and will not be able to help keep the correct course through their efforts.
Helping Build Personal Vision
Although you can explain your own vision and the vision of people up the line in the organization, you can't actually
Don't give the people you question the answers you want. You want them to develop their own responses, which might suggest additional questions that you'll ask. When you work this way, you allow people to make the same mental effort that you did. The process of answering the same questions (even if they didn't ask themselves) creates a personal vision for them.
You can ask the questions in groups, in one-on-one meetings, through memos, or any combination of these methods. As you do, you help develop the process of vision for everyone, and when you succeed, that turns into enormous opportunities for synergy. The group can actually create something together that is more than any of the members could have done alone.