A holiday should be a celebration or commemoration that also involves a day of rest, or at least a day off work and school. Many so-called "holidays" don't result in a true day off. For example Valentine's Day - whether it's viewed from a religious or commercial aspect, businesses and schools are open. The only "true" holidays are Memorial Day, Labor Day, MLK Day and Christmas.
Holiday has very widely varying definitions. To people in the United States holiday means something we celebrate. This could be Halloween, Thanksgiving, Christmas, and many others. In other countries Holiday means taking a vacation. If someone from the UK said they were going on holiday they mean that they are going on vacation. Holiday can be religious, non-religious, and nonsensical. This allows for a lot of interpretation as to what constitutes a holiday.