Friday remains a day of penance, even outside of Lent. Here is what the Code of Canon Law has to say:
All Christ’s faithful are obliged by divine law, each in his or her own way, to do penance. However, so that all may be joined together in a certain common practice of penance, days of penance are prescribed. On these days the faithful are in a special manner to devote themselves to prayer, to engage in works of piety and charity, and to deny themselves, by fulfilling their obligations more faithfully and especially by observing the fast and abstinence which the following canons prescribe. (CIC 1249)
This is the same as with worship. All the faithful are obliged by divine law to worship God and, so that all may join together in the corporate worship of God, days of worship (Sundays and holy days of obligation) have been instituted. The flip side of this is penance:
All are obliged to repent, and so that there may be corporate repentance toward God, days of penance have been set up, as in the Old Testament when the Jews proclaimed a national fast to do repent of their sins against God. Today, Friday is the chief day of penance since Christ died because of our sins on Friday, and Sunday is the chief day of worship, since Christ rose for our salvation on Sunday. (CIC 1250)
The days and times of penance for the universal Church are each Friday of the whole year and the season of Lent. . . . 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 o be observed on Ash Wednesday and Good Friday. . . . The law of abstinence binds those who have completed their 14th year. The law of fasting binds those who have attained their majority [i.e., 18 years; canon 97:1], until the beginning of their 60th year. Pastors of souls and parents are to ensure that even those who by reason of their age are not bound by the law of fasting and abstinence are taught the true meaning of penance. . . . The episcopal conference can determine more precisely the ways in which fasting and abstinence are to be observed. In place of abstinence or fasting it can substitute, in whole or in part, other forms of penance, especially works of charity and exercises of piety. (CIC 1251-1253)
Thus the law of abstinence from meat is still binding unless one’s national bishops’ conference has provided for alternate forms of penance. In the United States, the National Conference of Catholic Bishops has obtained permission from the Vatican for such substitution. Catholics are obliged to do some form of penance on Fridays and keep the day as per canon 1249, but now they can choose the form of penance they wish to do.