The Passover Week in Jerusalem, somewhere between 30 and 33 C.E., is the week in which Jesus enters Jerusalem in glory, adored by the crowds, riding on a donkey, spends time with his disciples in and around the temple, and then is crucified on Friday, just before the Jewish sabbath. Then, on the first day of the week, Jesus is seen alive in parts of Jerusalem, his tomb now empty.
The week begins in Matthew 21, Mark 11, Luke 19 and includes numerous teachings by Jesus about the coming kingdom of heaven and the end times.
Historically, Christians celebrate the Friday crucifixion as "Good Friday" and the Sunday resurrection as Easter Sunday. The celebrations of these days date back to probably the third century, if not earlier.
The last supper was apparently on Thursday, now celebrated as Maundy Thursday. Matthew 26:17 has the last supper occurring on the first day of the Feast of Unleavened Bread.
I've found a variety of interesting internet resources on the Passover Week. As always, Wikipedia is a good source. There is a Wikipedia article on the "Holy Week".
The Passover feast dates back to Exodus 12, when the tribe of Israel was expelled from Egypt. On that night (the 14th day of the month Nisan) the Jews sacrificed a lamb and spread its blood over their doorposts so that the Angel of Death would "pass over" their homes and spare them, while killing the first born son of the Egyptians.
A Catholic view of Passover is here. Another Christian view is here. A Jewish explanation can be found here and a Messianic Judaism view here or here.
Was Jesus, in the Last Supper, really celebrating the Passover Seder? A fairly detailed analysis of this question appears in this Biblical Archealogy article.
Tomorrow we return to Luke's account of the Passover Week.