The message count resets on your invoice date each month, which is listed under Settings.  Under the Subscription and Billing tab you can see additional details about the plan you are on.
On the Settings overview tab, you can also see how many messages of your plan limit that you have used so far.  The counters reset monthly and that is listed below.

The counters reset at midnight UTC time for all accounts.

If you need more messages, you can upgrade at any time.  Look for the green "Update Payment Method" on the Subscription and Billing tab. Or if you aren't ready to upgrade, once you hit your message allotment for the month you will then be billed 3 cents per message that you go over.  This will show in a large green header at the top of your screen to notify you of this as well.

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