The advantages to the employee working from home really differ from person to person. What is an advantage to one person might make no big difference to another.
For me the advantages are:
Travel Considerations
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- Reduced petrol consumption and car usage
- Dramatic saving on the time to get to my desk 
Working the Timezones
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- Free to vary my hours of work to match the timezones I work with
- Not having to drive home at unsociable hours when my road-vigilance skills are not at their optimum
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- Being saved from the distractions of the company offices
- Having something in common with my colleagues across the globe who work from home.
Quality of Life
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- Being able to use short breaks to advance personal projects from gardening, picking fruit, preparing a nice meal, shopping, domestic tasks (but must admit I'm not so hot on these) rather than spending the time drinking a bad coffee you didn't even want
- Being home to receive packages, deliveries, of if someone decides to offer me some apples from their garden, ...
- Developing relationships locally by shopping in our local area, chat to neighbours, ...
- Clearing your head with a short walk up and down the local scenic and peaceful lanes rather than two tours of the company office building
- Our house feels more like a home. Being a workaholic, if working in company offices, I would probably rarely see the house or my husband
We are all different so you will surely have other advantages that play to your life and family style