It does what it says on the tin: you get a home detox, with medication, in your home.
Don't forget, you only need a detox if you experience withdrawal symptoms when you stop drinking. Home detox is only safe if your home life is stable, and if you're in reasonably good physical and mental health. You'd also need a friend or relative around for the duration of the detox (although some higher end detox services have a nurse actually living with you for a week or so).
See here to read more about how detox works.
It gives you the chance to dry out in the privacy of your own home, without having to face other people in a hospital, rehab or clinic. Most NHS services offer home detox, but by going private you may get a quicker and more responsive service.
Remember, detox on its own is less likely to be successful in the long term if you don't have psychological help during and after the detox. It's just a small, if important, component of your treatment.
There aren't very many services at present that provide private home detox. Most services will be able to provide both detox and psychological help afterwards, or you can mix and match who you want to do the different parts of your treatment. Make sure that you're being assessed and treated by either a doctor or a nurse with experience in detox, and clarify what support is being provided as part of the package.
Make sure you meet the actual person who is going to be visiting you, and make sure you can get on with them. Don't be bounced into paying for detox over the phone before you've met anyone. You should get a lot of written information about your treatment, including a contract or agreement that outlines the responsibilities of both parties.