Reynolds was vital to the success of the peace process.
The basis of the ceasefire/peace was the belief of Gerry Adams and John Hume that any solution had to be an all-Ireland solution. In 1991 John Hume wrote
A Strategy for Peace and Justice in Ireland. Its idea was that the British government and the Unionists should acknowledge that the Irish people
might be united if there was a democratic mandate (ie the Unionists would not be forced into unity, but the north might one day voluntarily vote itself into a united ireland), and Republic of Ireland and the IRA/Sinn Fein would at the same time give up their constitutional claim to Northern Ireland (ie it would change its constitution and accept that the Unionists would not be forced to become part of a united Ireland if they didn't want to).
He took it to the Republic of Ireland government, who accepted it but didn't think it would work; and the British government outright rejected it.
Enter Albert Reynolds!
He ACCEPTED the Hume-Adams plan, and he did two things to help it succeed:
1. He persuaded President Clinton and the Americans to allow Gerry Adams to make a visit to the USA. The british government were against this, but Reynolds persuaded Clinton to ignore them. Adams visit established him as a politician (rather than a terrorist, as the British claimed) of world stature, important enough to meet the President - and if important enough to treat with the President of the USA, then surely important enought to be accepted at the megotiating table by the Prime Minister of the United Kingdom. Sulkily, the British were forced to listen to what Adams had to say.
2. He took a revised version of the Hume-Adams Plan (the 'Joint Declaration') to the British Prime Minister John Major and asked him to agree to it. Major refused. Reynolds insisted, and published the document, virtually forcing Major to agree. This then became the basis of the peace proess that followed. (You can read all about this
here.)