Historically, it comes from the fact that under the English domination, people were actually not allowed to wear green. Because to Irish, green represented their country (take a look at any landscape picture of Ireland and you know why), the English didn't want to see it.
Today, Irish (and non-Irish who are Irish for the day) wear green (usually a shamrock in the lapel) to symbolize their Irish identity and make up for when they feared wearing it and getting killed/
Under the English, if you were caught speaking Gaelic (the traditional Irish language) or wearing green, they would kill you. One of the more traditional Irish songs is called The Wearing of the Green. I've included the liyrics below:
O Paddy dear, an' did ye hear the news that's goin' round?
The shamrock is forbid by law to grow on Irish ground;
St. Patrick's Day no more we'll keep, his colour can't be seen,
For there's a cruel law agin the wearin' o' the Green.
I met with Napper Tandy, and he took me by the hand,
And he said, "How's poor old Ireland, and how does she stand?"
She's the most distressful country that ever yet was seen,
For they're hangin' men an' women there for the wearin' o' the Green.
Then since the colour we must wear is England's cruel red,
Sure Ireland's sons will ne'er forget the blood that they have shed,
You may take a shamrock from your hat and cast it on the sod,
It will take root and flourish there though underfoot it's trod.
When law can stop the blades of grass from growin' as they grow,
And when the leaves in summer-time their colour dare not show,
Then will I change the colour, too, I wear in my caubeen
But 'till that day, please God, I'll stick to wearin' o' the Green.
But if at last our colour should be torn from Ireland's heart,
Her sons with shame and sorrow from the dear old isle will part;
I've heard a whisper of a land that lies beyond the sea
Where rich and poor stand equal in the light of freedom's day.
O Erin, must we leave you driven by a tyrant's hand?
Must we ask a mother's blessing from a strange and distant land?
Where the cruel cross of England shall nevermore be seen,
And where, please God, we'll live and die still wearin' o' the green!