The lex loci celebrationis is the Latin term for "law of the place where the marriage is celebrated" in the Conflict of Laws. Conflict is the branch of public law regulating all lawsuits involving a "foreign" law element where a difference in result will occur depending on which laws are applied.
The lex loci celebrationis is a choice of law rule applied to cases testing the validity of a marriage. For example, suppose that a person domiciled in Scotland and a person habitually resident in France, both being of the Islamic faith, go through an Islamic marriage ceremony in Pakistan where their respective families originated. This ceremony is not registered with the Pakistani authorities but they initially establish a matrimonial home in Karachi. After a year, they return to Europe. For immigration and other purposes, whether they are now husband and wife would be referred to the law of Pakistan because that is the most immediately relevant law by which to decide precisely the nature of the ceremony they went through and the effect of failing to register it. If the ceremony was in fact sufficient to create a valid marriage under Pakistani law and there are no public policy issues raised under their personal laws of lex domicilii or habitual residence, and under the lex fori, they will be treated a validly married for all purposes, i.e. it will be an in rem outcome.