Why is Poson Poya important to Buddhists in Sri Lanka? It is because it was on a Poson Poya Day that Arahath Mahinda came from India and met the Sri Lankan monarch Devanampiyatiisa at Missaka Pabbata now known as Mihintale.
Arahath Mahinda preached the Dhamma to King Devanampiyatissa and his retinue and converted them to Buddhism and established Buddhism in Sri Lanka. This happened in 236 BC (3rd century BC).
On this Poson Poya Day King Devanampiyatissa went deer hunting. He was accompanied by 40,000 men. His chosen location to hunt was Missaka Pabbata or the present Mihintale. (Missaka Pabbata got this name as it is formed of stone and sand).
According to legend the deity or god in charge of Mihintale changed himself to a deer and crossed the King’s path and stared to graze. The King thought it was not good to shoot at a grazing deer and made a noise to distract it from feeding and make it run. The deer ran and the King gave chase.
As he started to chase the deer the King heard someone saying "Tissa, Tissa".
He looked up in surprise and saw Arahath Mahinda and his entourage. The Arahath introduced himself as the son of Emperor Ashoka of India. Now, King Devanampiyatissa knew the Emperor Ashoka through correspondence and also knew that the Emperor had renounced was and become a Buddhist.
The King threw down his bow and arrows and his retinue did the same. They then sat to hear what Arahath Mahinda had to say.
The Arahath first asked the King some questions and then he preached the Chullahaththi Padopama Suthraya and King Devanampiyatissa and his 40,000 men became Buddhists. The King invited Arahath Mahinda and his retinue to come to the Royal Palace for alms the next day and returned to his palace in his capital city of Anuradhapura.
Sources: Wikipedia, Buddhism in Sri Lanka by H.R.Perera, Daily News,https// trip2srilanka.com