Fat Tuesday (also known as Mardi Gras or Shrove Tuesday) is customarily a time to indulge in vast amounts of food and to participate in parties and parades on the days before Ash Wednesday.
This practice has a long tradition in most of Europe and was brought to the United States by many immigrants.
However, bishops and priests saw the excesses of these carnival celebrations and made efforts to curtail them, encouraging Catholic to participate in Eucharistic adoration instead.
The Catholic Encyclopedia explains that there was once even a plenary indulgence for anyone who attended adoration with the Eucharist exposed in the days preceding Ash Wednesday:
The Church repeatedly made efforts to check the excesses of the carnival, especially in Italy. During the 16th century in particular a special form of the Forty Hours Prayer was instituted in many places on the Monday and Tuesday of Shrovetide, partly to draw the people away from these dangerous occasions of sin, partly to make expiation for the excesses committed. By a special constitution addressed by Benedict XIV to the archbishops and bishops of the Papal States, and headed "Super Bacchanalibus," a plenary indulgence was granted in 1747 to those who took part in the Exposition of the Blessed Sacrament which was to be carried out daily for three days during the carnival season.
The usual conditions for obtaining a plenary indulgence are the confession of sins and the reception of Holy Communion within one week. Often this also includes praying for the intentions of the Holy Father.
While there has not been any recent proclamation affirming this particular indulgence, Catholics are still encouraged to attend Eucharistic adoration during these days of Mardi Gras.