St Patrick's Day
If you go for a walk in Ireland on the 17th March you would probably see plenty of shamrocks, and people wearing green, drinking beer or participating in a parade, on the occasion of Saint Patrick's Day ! 
Basically, Saint Patrick's Day is a Christian celebration, to commemorate Saint Patrick, but today it's a kind of National day, where people celebrate more generally, the whole Irish culture. It's celebrated throughout Great Britain, Canada, in the United States etc.
Saint Patrick's Day as well as being a public holiday marks the middle of lent, the Christian season of fasting.
Indeed, it's a day where everything is allowed, there are no restrictions, people can do what they want, like eating what they like or drinking alcohol etc.!
Who was Saint Patrick?
Saint Patrick, the patron saint of Ireland is famous for having brought Christianity to Ireland.
The story of St Patrick is uncertain from an historical point of view, actually, we don't exactly know when he was born, probably around 385AD, you just have to keep in mind that he lived around the fourth century, but we can suppose that he died on the 17th March, the date of the festival in fact.
Surprisingly, he was not born in Ireland, according to a legend, he was born in Roman England. When he was about 16, he was captured by Irish pirates and he was taken as a slave to Ireland. From there he had holy vision, telling him to go back home, so he escaped and became a cleric. I will not detail his whole life but you have to remember that according to the legend, Saint Patrick dedicated his entire life to God and to the Irish people.
Why does people wear green on this day?
For the question of why people wear green, originally, green was not used for Saint Patrick's Day, and it was long considered unlucky because this color was associated with Leprechauns, so it was blue that was linked to Saint Patrick. Then the green, from the Irish flag finally prevailed, but a mistake remains because, the green on the Irish flag is a Saint Patrick symbol as well.
Indeed, green also symbolizes the shamrock, because legend says that Saint Patrick used a little Shamrock (a plant with a leaf that is divided into 3 parts) to explain the Holy Trinity to the pagans (The Father, the Son and the Holy Spirit).
How is celebrated? 
On St Patrick’s day, there are many things to do, people dance in festivals, concerts, but the main event in this occasion would probably be the parade, with the biggest one in Dublin.
People also go to the pub to drink beer (Guinness) and traditional alcohol like Irish whiskey, but to eat some traditional recipes as well, like Corned Beef and Cabbage with Herb Buttered Potatoes
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Typical drinking music to imagine a pub atmosphere...