In North America a vacation is a holiday period between terms in university and law courts. It also means a period granted by your employer when you don't have to go to work, but are usually still paid (a paid vacation). The usual period is around 2 - 3 weeks, although long serving employees may get more.
A holiday is generally used to mean a statutory holiday (such as Easter, Christmas, Thanksgiving, etc).

In the UK they generally don't use "vacation", but use holiday to mean any period when you don't have to go to work or school. Also they use the term "bank holiday" to refer to a day when banks are officially closed, kept as a public holiday.