What did palm branch signify in the Bible?

Answer

Palm branches are associated in the Bible with Palm Sunday, which John Shelby Spong (Jesus for the NonReligious) says came from a Jewish festival actually held at a very different time of year:
The ]ewish eight day celebration of the harvest, known as Sukkoth, and also called the Festival of the Tabernacles or Booths, was probably the most popular holiday among the Jews in the first century. In the observance of Sukkoth, worshippers processed through Jerusalem and in the Temple, waving a bunch of leafy branches made of willow, myrtle and palm. As they waved these branches in that procession, the worshippers recited words from Psalm 118, the psalm normally used at Sukkoth. Among these words were "Save us, we beseech you, O Lord." Save us in Hebrew is hosianna or 'hosanna'. This is typically followed by "Blessed is the one who comes in the name of the Lord. (Psalm 118:25-6)."

Mark's Gospel was the earliest of the New Testament gospels. It took the Sukkoth traditions and transferred them from autumn to the Passover season for the procession story. Mark 11:8 says (NAB), "Many people spread their cloaks on the road, and others spread leafy branches that they had cut from the fields." The words used at the Sukkoth are reflected in Mark 11:9: "And they that went before, and they that followed, cried, saying, Hosanna; Blessed be he that cometh in the name of the Lord." Because the Passover season is too early for 'leafy branches' (except palms), John actually says 'palm branches', creating our modern tradition of Palm Sunday.