The Romans began each year by making promises to the god Janus, for whom the month of January is named.
In the Medieval era, the knights took the “peacock vow” at the end of the Christmas season each year to re-affirm their commitment to chivalry.
At watchnight services, many Christians prepare for the year ahead by praying and making these resolutions.
There are other religious parallels to this tradition. During Judaism’s New Year, Rosh Hashanah, through the High Holidays and culminating in Yom Kippur (the Day of Atonement), one is to reflect upon one’s wrongdoings over the year and both seek and offer forgiveness.
People may act similarly during the Catholic fasting period of Lent, though the motive behind this holiday is more of sacrifice than of responsibility, in fact the practice of New Year’s resolutions partially came from the Lenten sacrifices.
The concept, regardless of creed, is to reflect upon self-improvement annually.