Until Catholic Emancipation in 1829, in theory the only valid marriages were those carried out by the state church, the Church of Ireland. In practice this was widely ignored. For many years before then, Catholic priests had been recording marriages.
Until 1845, almost all marriage registers record a bare minimum of information: the date and the people marrying. Catholic registers also supply the names of witnesses and, sometimes, an address. Church of Ireland registers regularly supply only the names of the two people and the date.
After 1845, Church of Ireland clergy began to act as civil registrars in the recording of all non-Catholic marriages. Civil marriage records include precise addresses and, most important for family history, the names of the fathers of both people getting married.
From the mid-1850s, most Dublin city Catholic parishes also began to record the names and addresses, not just of fathers, but also mothers, along with their precise address. In a few other locations (Kerry, in particular) officiating priests began to do the same.
From 1864, all marriages have both a civil and religious record. Usually, the civil record is more informative. The big exception remains Dublin city Catholic marriages, with details of both parents and their addresses.
The Church of Ireland had effective ownership of all graveyards until the early 19th century, though many Catholic families retained traditional burial rights. Perhaps for this reason, most Catholic parishes did not keep burial registers, while almost all Church of Ireland parishes did. In any case, burial records are rarely of much value for family history, almost never specifying family connections.