While I'm using the Trello application online, there is a number that appears next to my board tab. It looks like there is a notification or message that I'm missing but I can't figure out how to access it. I just added someone to the board and they are now able to access the information but I was curious as to what this number was.
A screen shot might help explain what you are asking about. Short of that...
Generally, with Trello, anything new or different appearing on your Trello screen can be clicked for more information.
Example: The notification bell in the top right corner turns red when changes made by other people or due date notices for you are available to read. Click the bell and the notification bar opens where you can read the updates. Click away from the bar to close it and clear the notification notice.
I suspect the numbers are related how many unread updates have happened since you last read them.