For most Christians the most special day of the week is Sunday. It was the day on which Jesus was raised from the dead, and Christians have held a weekly worship service on that day for many centuries. In countries with a Christian heritage Sunday is a day off to allow Christians to celebrate.
While Sunday is normally the day of worship, many Christians believe it to be a matter of tradition rather than a requirement of God. Christians that live in countries where where religious services are usually held on another day, such as Saturday in Jewish countries or Friday for Islamic countries, will often hold services on those days because it is easier to attend. ("On that day" may mean "the evening before" in countries where the traditional day runs from sundown to sundown).
One church that treats Friday specially is the Roman Catholic church. Friday is a special fast day, on which people abstain from meat. Canon law says:
Can. 1250 The penitential days and times in the universal Church are every Friday of the whole year and the season of Lent.
Can. 1251 Abstinence from meat, or from some other food as determined by the Episcopal Conference, is to be observed on all Fridays, unless a solemnity should fall on a Friday. Abstinence and fasting are to be observed on Ash Wednesday and Good Friday.
Other denominations like Anglicans and Methodists do similar. See Friday Fast.