How does it work.

Depends what you want to do. You could have it going to Dropbox, and then the database in Dropbox can be accessed via a browser on any device, whether or not you own it. You would need to remember the Dropbox password as well as the 1Password master password. This approach is called 1Password Anywhere.

But if you only want to use it on devices that you own, then you can actually sync the databases and access much better. You need a license for each OS.

So, a Mac OS X license, a Windows license, and an iOS license. The iOS license is free in its basic form, with an in-app purchase offering extra features. There is a bundle for Mac and Windows which discounts the price for two separate licenses.

On the Mac, you can get 1PW either direct from AgileBits web store or from Apple's App Store. The advantage of buying from the App Store is that you can use iCloud sync between the Mac and the iOS devices. But iCloud does not work on Windows, and very many people find Dropbox sync to be at least as good as iCloud. One advantage of buying direct from AgileBits is that you there be an upgrade for which a charge is made (which there will be some day, though it might well be a couple of years away), they can offer a discount to existing users, which can't be done on the App Store.

The version direct from AgileBits offers a thirty-day free trial, which can't be done through the App Store. With a bit of work, one can start with the trial and move the passwords over if you want to buy the App Store version.