I'll try:
In your profile, you can select look and layout preferences (LHS menu). On this page, you can change your theme - the way the forum looks. I have selectd the Classic YaBB SE Theme.
When you go back to the forum home page (that lists all the sub-forums - Behaviour, Puppies, etc) each of these has a coloured blob on the LHS on the sub-forum name. If there are any new posts in that sub-forum since you last looked at it, it goes a different colour.
when you click on the sub-forum name, you see a list of threads/topics. If any of them have got new posts since you last looked, they have the word NEW next to them
So, from the home page, you can scan the list of sub-forums to see any with new posts in; open the sub-forum, and see all the topics with new posts. Each time you return to the home page, it will always show you which sub-forums have new posts since you last looked in there, even those posted during current visit