DanMayo is right. The green chip appears beside forums that have new postings since your last visit. If you see green chips, then clicking New Posts at the top will display them.
I find that 'New Posts' is the easiest way to stay up to date on the conversations. However, sometimes I find that I get distracted before reading all the new posts. If it's been at least 15 minutes, the software assumes you've read all the new posts you were interested in, and they'll no longer appear as new, whether you read them or not.
When that happens, here's a useful way to adapt: Under 'Quick Links', there is a 'Today's Posts' choice that will list only things posted since midnight.