What the balance is
Your account holds a number of support tickets. It belongs to the company, not to a person: everyone holding a seat draws on the same balance, and it does not reset monthly.
It is shown in two places, and they are always the same number. In the band at the top of every portal page, beside your company name, as "25 support tickets available". And on your dashboard, as the Support tickets available tile.

What spends one
Opening a new ticket spends exactly one, at the moment you submit the form.
Nothing else costs anything. Replying to a ticket is free, however many times. Attaching logs or a configuration is free. A ticket that runs for three weeks costs the same one as a ticket answered in an hour. Reading, searching and downloading your licences are all free.
If something goes wrong while the ticket is being saved, the ticket is not created and the balance is put back. You are never charged for a ticket that does not exist.
What the tile is telling you
The tile changes as the balance falls, so that running out is never a surprise. Above two it simply shows the number. At two or fewer it says "Running low". At zero it says "No tickets available".

At zero
With no tickets left you cannot open a new one. The New ticket page says so instead of showing the form — deliberately, so that nobody writes out a problem, attaches their logs, presses Submit and only then finds out.
Everything else keeps working. Every ticket you already have stays open and you can still reply to all of them, so a conversation in progress is never cut off by the balance running out. Your licences, messages and downloads are all unaffected.
Getting more
Ask BlueDot. The "Buy support tickets" button on the dashboard, and the one on the New ticket page when the balance is zero, both take you to the support contact form today. Send us a note there and we will top the account up; the new balance shows immediately. A store where you can buy them yourself is on the way.