The four Gospels make it clear that Jesus was crucified in conjunction with the Jewish Passover (Matthew 26:17-19; Mark 14:12-16; Luke 22:7-15; John 18:28,39; 19:14). The four Gospels also make it clear that Jesus was raised from the dead three days later, on the first day of the week (Matthew 28:1; Mark 16:2,9; Luke 24:1; John 20:1,19). Biblically speaking, then, Christ's resurrection should be celebrated on the first Sunday after the Jewish Passover meal. However, this is not the case. Easter is celebrated on the first Sunday after the first full moon after the vernal equinox (the first day of spring). This method of determining the date of Easter often results in Easter being before Passover and/or displaced far from Passover. Easter can potentially be observed anywhere between March 22 and April 25.
In church history, there was a significant amount of debate that went into determining when Easter would be observed. As a background, please read our article on the origins of Easter. Dating Easter in conjunction with the vernal equinox and full moon had nothing to do with the biblical account of Christ's resurrection or the Passover. The only thing that is explicitly biblical regarding when Easter is now observed is the fact that Easter is always on a Sunday.
The Bible does not instruct Christians to set aside a day to celebrate Christ's resurrection. At the same time, the resurrection is most assuredly worth celebrating (1 Corinthians chapter 15). Celebration of Christ's resurrection, then, is a matter of Christian freedom. Christians are free to celebrate the day of Christ's resurrection and are free to refrain from celebrating. Since it is a matter of Christian freedom and not a biblical command, it would seem that there is also freedom as to precisely when the celebration of Christ's resurrection is observed. Just as with Christmas, the exact date is not important. It is the fact that Christ was resurrected that is important. Christians are free to follow the traditional dating system for Easter, thereby observing Easter on the first Sunday after the first full moon after the vernal equinox.