It is not, under current law, the day a Cardinal turns 80.
The relevant portion of Universi Dominici Gregis (John Paul II, 22 Feb 1996) is in paragraph 33:
The right to elect the Roman Pontiff belongs exclusively to the Cardinals of Holy Roman Church, with the exception of those who have reached their eightieth birthday before the day of the Roman Pontiff's death or the day when the Apostolic See becomes vacant.
So the key factor is the age of the Cardinal on the day the Holy See becomes vacant. If he turned 80 before that day, he is not eligible to vote. If the Cardinal turns 80 on or after that day, he remains eligible to vote until that Conclave is completed.
I should note that this is a change from the law issued by Pope Paul VI.
Under Ingravescentem Aetatem (Paul VI, 21 Nov 1970) effective 1 Jan 1971, a Cardinal lost the right to vote upon reaching the age of 80 if the Conclave had not already started.
So the key factor under that old rule was the age of the Cardinal on the day the Conclave began. If he turned 80 on or before that day, he was not eligible to vote. If the Cardinal turned 80 after the Conclave began, he retained the right until that Conclave was complete.
Prior to 1971, there was no age limit. A Cardinal of any age could vote in a Conclave.
Now back to current law and a quick summary.
For the purpose of lists showing Cardinals that would be eligible to vote in a Conclave: a Cardinal should be removed from such a list the day after they turn 80 years old.
The exception is when the Holy See is vacant, then the Cardinal should only be removed from such a list the day the Conclave is completed.
So why shouldn't a Cardinal be removed the day they turn 80?
If the Pope, God forbid, were to die later that same day, the Cardinal is still eligible to vote in the subsequent Conclave!