The three decades long sectarian conflict, which became known as The Troubles, brought violence to the streets of Northern Ireland, Great Britain and Ireland.
The Duke and Duchess of Cambridge are attending a reception on Wednesday night hosted by the Irish Foreign Minister, Simon Coveney.
The Prince is expected to say: "Growing up I remember seeing the Troubles that took place, which affected so many people across the UK and Ireland."
William will call that visit a "truly profound moment" for them.
"It was a reminder of the complexity of our shared history, and as my grandmother said during her visit in 2011, 'our islands have experienced more than their fair share of heartache and turbulence'."
The Duke of Cambridge is also expected to touch on current political tensions over Britain's decision to leave the European Union.
Ireland is the only country in the EU with which the United Kingdom shares a land border.
The negotiations between the UK and the 27 members of the EU were dramatically delayed over the difficulties of the Northern Ireland issue and the delicacy of the Good Friday peace process which started to bring an end to the 30 years of violence.
William will add: "It was also a reminder of how far we have come. It is right that we continue to remember those who suffered as a consequence of our troubled past. And whilst many wrongs have been done, it is important that we are not bound by these."