While most people will probably prefer to use their smart phone to sync Microsoft Band with the Microsoft Health service and install firmware updates, you don't actually need to use a mobile app all of the time. Instead, you can use a desktop sync app for Windows or Mac, which works as a companion to, and not a replacement of, the mobile app.
This is a useful option for those who will be charging their Band every day, say at work, and can connect the Band charger to their PC. The Windows and Mac sync apps for Microsoft Band perform their magic over USB, not wirelessly. It's like killing two birds with one stone.
One upside to these apps is that they work in conjunction with a mobile app version of the sync software (where it's called Microsoft Health, oddly) on Android, iPhone, or Windows Phone. (Which is nice, because you can't use the Microsoft Band app on multiple handsets.) Indeed, this is by design: The desktop apps are pretty limited and are designed as companions to the mobile apps, not as desktop-based replacements.
Installation and setup is simple, and works much as it does with the mobile apps: You sign into your Microsoft account, and if you're associating a Band with that account for the first time, you may be asked to fill in some basic profile info (name, birthdate, height and weight and so on). After that, the application will sync your Band's data with Microsoft Health when you connect and charge it via your PC.
The app can also be used to:
Install a firmware update. The app will alert you when one is available, and you can click the Check for Updates button to check manually.
Edit your profile. When you've lost weight or grown a couple of inches, click My Profile to make the appropriate changes.
Configure application settings. Click Settings to configure two sync application settings (i.e. this isn't for configuring the Band): Auto sync when connected (on by default) and open automatically at start (also on by default).
Even if you do use one of these app, you'll still need to continue using the Microsoft Health app on Android, iPhone or Windows Phone, as those mobile apps provide far more functionality, including a full activity history, finding and installing workouts, setting Band preferences, connecting other mobile apps (RunKeeper and so on), and personalizing the Band (determining which tiles appear and where, configuring a theme and the like), and more.
You can download Microsoft Band sync app for Windows from the Microsoft web site. This app requires Windows 7 with Service Pack 1 or newer. This is a desktop application, so it will not run on Windows RT.
You can download Microsoft Band sync app for Mac from the Mac App Store. This app requires Mac OS X 10.9 or later.