It's about as big as a big wristwatch. They tend to be grey plastic. I wish I had brought one with me. They're not particularly obtrusive any more. Your analogy of the wristwatch is quite accurate.
The monitoring technology can be packaged into something quite small now, but the strap is an important piece of the technology because it's usually got an optical fibre in it. It is the breaking of the optical fibre that tells the monitoring company the tag has been tampered with.
It isn't just the body of the tag; it can also be the strap that is important. Some companies make straps that have steel in them, so they're harder to remove.