It is one calendar day and you can use it as much as you like within that day. Your Paris Visite Card counts from the day of first use (whether you activate it in the morning, afternoon, or evening) until midnight on the last day of validity.
For example, if you have a one-day card and you start using it at 8PM, it will be valid until 12PM on that day, not 8PM the following day. If you start using the card at 6AM, you will still have until 12PM on that day to use it.
Therefore, in order to get the most out of your card, it is best to start using it in the morning as this allows you to get the most out of it. If you need a late trip, we recommend purchasing a single journey in Paris, rather than wasting an entire day of your Paris Visite Card.