My understanding of the word is that it is a corruption of the Irish Gaelic word "slainte" which means "to your health". A planxty then is a tune to the health of the person that O'Carolan wrote the tune for. He was the last of the great Bardic harpers. As was the custom, he would travel from home to home, and the resident would have to put him up. If he felt the hospitality was suitable, or some event occurred that he enjoyed, he would write a "planxty" to that person. My two favorites are Planxty Irwin (I love playing this on my 60's vintage Guild 12 string) and Planxty Mary O'Neill.My source for this is a performer from Ulster who passed it on to me. Best I can do.
Mick