i think what youre talking about is an icon indicating that you have a "saved search". you must have opened your browser at one point and saved the page while it was loading. you can go into your messages list you should see it there and delete it and then the icon will disappear.
If it is a circle with what looks like an arrow going into it, it is a notification that you have an app with an update. The number indicates the number of apps with uodates. To access them, go to your messages, there should be a message from that app.