I've noticed that next to some threads there's a little white check in a blue box, but if I recall correctly it was only next to my own threads. Is that an indicator showing that it is your own thread, or does it have a different meaning?
If you're talking about this icon , then that's just a button indicating that there are new posts on the thread that you haven't seen. If you click it, it will take you to the first new post on the thread. If you're talking about a different icon then I'm not sure which you're talking about.
And if you're talking about this icon , then that's just an indicator that you are subscribed to a thread. I think by default you subscribe to threads you create, and you can choose to subscribe to other threads too. You can subscribe to an individual thread using the "Thread Tools" menu above the top post, and you can subscribe to any thread you post in automatically by going to "Quick Links" and then "Edit Options" in the navigation bar at the top of the page; scroll down and change the "Default Thread Subscription Mode". Subscribing to threads is useful because then you can keep track of threads you are interested in and you can see new posts in them easily by going to "Quick Links" and then "Subscribed Threads". If you're talking about a different icon then I'm not sure which you're talking about.