How does running a restaurant relate to running for council?

The restaurant business is a microcosm of the whole business world. Probably one of the most complicated anywhere.
Here are many of the things involved:
As a Chef, You are a 

• manufacturer,  distributor, expediter
• employer, pr manager, creative director
• accountant, planner & forcaster
• sanitation and safety manager
• maintenance engineer and and traffic control expert.

These are just the start. You have to hire and manage staff, plan the hours according to forecast needs, manage the payroll and labour costs.
You have to learn marketing, advertising and public relations.
You have to create products from raw materials you source and produce a desirable and consistent product.
Understanding you market is vital, and you must constantly update your data.
You need to accurately track your sales, income, tax amounts, profits, banking in order to plan for tomorrow and the future.
A huge list of capital equipment and tools must be maintained and monitored for life expectancy, and you must plan to have replacement cost monies put aside for that.
Inventory control and stock rotation are daily chores. As are negotiating best quality and pricing from not just your suppliers but your subcontractors and service personal.
You have to be able to prepare and fully understand your P & L statements.
In between all of that you are wearing a dozen other hats at any moment. The more successful you become the more you have to be able to take the heat in the kitchen. 
You don't need to be expert at all of these thing, but you need to know enough, that no one can pull the wool over your eyes.
And you need to know how to attract people "more" capable than yourself to handle the jobs best.

Above all you have to truly like and enjoy interacting with the public.

When you take a good long look at it, these are exactly the skills that make for a good Town Councilor.