V-E day, is that the 8th or the 9th of may?

Why are there two dates for the same event?

Close to midnight

It was late in the evening on may 8th, 1945. A German delegation - headed by Field Marshal Wilhelm Keitel - signed a document of unconditional surrender.
He did so under the watchful eye of Marshal Georgy Zhukov and a SHAEF delegation. World war 2 was over in Europe!
Keitel signed the surrender document shortly before midnight, Berlin time, on the 8th of may. The ruins of the Reichstag were still smouldering.
Word went out immediately. When the news reached Moscow, it as already past midnight there; so it was already the 9th of may for the Soviets.
Everywhere, people took to the streets en masseĀ and celebrated. Finally, there was an end to the hell that people had endured during nearly 6 years of war.
Most Western countries had already started celebrating V-E day on the 8th, because General Alfred Jodl had already surrendered the German armed forces to the allies by then.

Commemorate and celebrate

Does it matter which moment you point to as the precise moment the war ended?
Not really. Jodls and Keitels signatures were both delivered on the 8th, so if you live in western Europe you'll probably celebrate on the 8th.
Time zones and coincidence made it the 9th of may for countries in the USSR.
What matters is that we all commemorate the victims and celebrate the victory over fascism; it had claimed some 60 million war and genocide victims.
It also matters that it all happened in the space of one day. Maybe the thing that stands out these days is that we all celebrate the end of the most bloody war in history.
The war wasn't over yet for millions of people in the Pacific, where the fire was still burning. There would be hundreds of thousands more victims before the end on august 15th, 1945.
In spite of this, the 8th and 9th of may of 1945 were a good moment to have a party or two in every time zone.

Maybe it's difficult to imagine today, but V-E day marked a shared victory by the USSR, the USA, Britain and France (and a lot more countries).
They had been cooperating very closely to win the war, something that sadly seems to have been forgotten over time.