The process of planning was not dissimilar to any business planning exercise I have been involved in. From this simple situation we can deduce that planning is an important process to help us achieve goals that have to be accomplished by a group of people in more or less the same time framework with a certain set of resources. We can see that it is an emergent and iterative process through which ideas are proposed, shared, evaluated, refined or rejected with the people who need to be involved. I also noticed that the planning process 'degenerated into actually doing stuff'. For example when we discussed the possibility of going to Australia my wife had to check out when she could take leave and I got involved in looking at possible flights and routes.
When I worked for an organisation I used to make detailed and explicit plans to make myself and my team accountable to managers and project boards - in fact I still do this for Lifewide Education at the scale of an annual plan with some broad goals and targets. But at the nitty gritty scale, 'working plans' tend to be broad headings that act as a prompt for doing stuff and the what it is that is done generally emerges in the act of doing. So planning and doing at the level at which it really matters are intimate partners.
So why do we plan? I guess we can all think of many reasons. It's about trying to see into the future and appreciate how you might influence aspects of the future by doing things that will help you progress towards that future. In this sense planning holds the visions of your purposes and what you want to achieve in your life and when it is a collaborative thing it serves the social purpose of creating a shared vision of what you want to achieve together.