Okay, couple of things to show here. =]
I'll start by saying that the forum's icon (the bug for this forum, for example) being lit up is
the 'new topics' marker.
When the icons are greyed out you're all caught up. When they're not, you're not.
In the forum itself the topics have two markers, as shown below.
In purple is the topics' icon. This is where you'll see marks to show a topic is a sticky or an announcement, for example. The icon circled is dark grey (for 'new posts'), whereas the one for the topic below it is light grey ('no new posts').
Secondly there is the [NEW] text in yellow. This also marks a topic as having new posts, but is also a link. If you click it, it will take you to the first post that you haven't read (more on that later).
Lastly in blue is the link to the most recent post - this will bypass any other posts you've not read yet, and take you straight to the last post on the topic.
Now, how does the board know what you've read? Well, it does and it doesn't.
New members see no new posts at all, because as a new member they've not read anything so nothing 'new' has been posted.
For the rest of us, every time we read a topic an entry is made in the database that tells the board where you've read to. It does this by page number and not by individual post, so if you start reading a topic and then leave your metaphorical bookmark might be in slightly the wrong place, so to speak.
Each page you open in a topic is marked as 'read', but not the topic (yet). So if you log in and a topic has three pages of new posts, reading the first two pages will leave the topic leave marked as having new posts, because you haven't fully caught up yet. This in turn will leave the forum marked as having new posts, for the same reason. Once you open (and it's assumed read) the last page on a topic, the board knows you're caught up, and removes the 'new posts' status.
If any of the above doesn't make sense let me know!
Now onto the next bit - clearing the 'new' posts without reading them.
If a forum is full of topics that you don't want to read but don't want to see as 'new', you use the 'mark as read' button. Using the button circled below will clear the 'new posts' status from every topic in that particular forum, which leaves the forum icon grey.
(this button isn't visible in portrait on small displays)
((note the is a separate button that will subscribe you to the forum, so you get a notification any time a new post is made in it. Not
what we're looking for here!))
Lastly, if you want to clear the 'new' status for every topic
on the whole board, there's a button for that too!
This one will mark everything as read, leaving all the icons grey.
The biggest problem with a time-based removal of the 'new' status would be picking up where you left off.
If I post in a topic, and you don't read it for a month (so it marks itself as no longer new), then someone else replies, and you go to the first 'new' post, the board would send you to the newest reply, not mine, even though technically mine is the first unread post.