What does the President of Ireland do?

It's a rather ridiculous and redundant office.
It's  predominantly ceremonial with a few limited discretionary powers and entitlements. Most of the time the President simply attends functions , receives ambassadors and invites various groups to the Presidential Palace to tell them how wonderful they are .
They issue statements of sympathy after various tragedies and occasionally travel around the country to clap the peasants on the back .
It has been demonstrated that  whatever  a President  does is already being done or could be usefully and more cheaply delegated to various existing individuals or bodies.
A pointless  waste of money.

Might have agreed with you lads 20 years ago , but not now .  The last 2 incumbents of the office have done a power of good with limited jurisdictional power .  Huge admiration for the 2 first ladies in question , have put us men to shame ( we do aspire traditionally to "run the country " , but pretty poorly given the opportunities afforded by the economics of the situation ).

The recent  State visit was down to Mary McAleese by all reports  , resounding success , and those who objected to it or did not participate deserve a big thumbs down .  Cant say I am filled with great anticipation regarding whoever gets the next nod , but history will have to adjudicate on that one . Hard acts to follow .

Compared with the money wasted down south by FF mainly and with the amount spent up north in fairly pointless enquiries ( where anyone with savvy knew what had happened ) , any Presidential expenditure over last 20 years has been great value in my book  , and it has benefitted south and north .

The world does watch , big audience in USA , and commented on by their president during his drop in . We are a very small cog in the machine  , but world spin off from seeming to try to act responsibly and hospitably towards neighbours is noted . Works both ways too .