What determines when a user was “seen”?
This value is changing all the time and I can't figure out what it is exactly.
The "seen" field in your profile displays the last time that you were "seen" on or by the site. In other words, it indicates your last activity on that particular Stack Exchange site.
It changes all the time because when you're doing things on the site, it's "seeing" you. It's really not all that useful for you, because you know when you've last been active on the site! But it's great for other users who are curious when you last logged on.