The Republic of Ireland is not part of the Schengen area, nor the United Kingdom. Whether you need a visa to enter Ireland depends on what country you're from. You can find out if you are subject to visa requirements to enter Ireland based on your nationality on the Irish Immigration website.
You may be able to visit Ireland without applying for a separate Irish visa, if you have an eligible UK (short stay) visitor visa and you are a citizen of an approved country. Read how this works under the Short Stay Visa Waiver Programme.
Irish visas may be single- or multiple-entry and allow the holder to spend no more than 90 days in Ireland.