Wikipedia
Closed communion is the practice of restricting the serving of the elements of Holy Communion (also called Eucharist, The Lord's Supper) to those who are members in good standing of a particular church, denomination, sect, or congregation. Though the meaning of the term varies slightly in different Christian theological traditions, it generally means that a church or denomination limits participation either to members of their own church, members of their own denomination, or members of some specific class (e.g., baptized members of evangelical churches). See also intercommunion.
A closed-communion church is one that (perhaps with exceptions in unusual circumstances) excludes non-members from receiving communion. This is the practice of all churches dating from before the Protestant Reformation and also of some Protestant church such as some Lutherans and Baptists. Non ELCA Lutherans in the US require catechetical instruction for all people, even members from other Lutheran Churches, before receiving the Eucharist while some Baptist churches require part membership while others even require full membership before participating in the communion service.
Churches which practice open communion allow all Christians to partake in the Lord's Supper, with membership in a particular Christian community not required to receive bread and wine, in contrast to pre-Reformation churches, which hold that what is received in their celebrations ceases to be bread and wine.