You can click the Mark-Forums-Read button in the upper left corner
There's two new post indicators
One is in the forum sub-menu to the left under Forums beside New-Posts button, it indicates the number of unread posts. To clear that number you can view the posts or click New-Posts then click Mark-As-Read.
Then there is an alert to the far right beside the flag icon, which indicates changes to posts you participated in, new posts in forums you are watching, and other alerts as checked in alert-preferences. To clear that number you can mouse over the flag icon to display the alerts, then those alerts should not be counted as new alerts.