When Jesus makes his triumphal entry into Jerusalem (Palm Sunday), what is the significance or symbolism of the palm fronds?

You are referring to the event recorded in John 12:13 (Matthew 21:8, Mark 11:8, and Luke 19 mention nothing about palms, perhaps because Jericho, from which Jesus had just come, was the City of Palms, as in Deuteronomy 34:3).

In Jewish biblical thought, palm branches are fraught with meaning:

1. A palm frond can symbolize the Jewish leaders (Isaiah 9:14, 19:15). Jesus is claiming to be Israel's true leader -- especially as he enters on a donkey, the animal of choice for kings and judges.
2. Fronds were used at the start of the Feast of Tabernacles (Sukkoth, or Feast of Booths) to construct the temporary shelters in which committed Jews lived during the week-long celebration (Leviticus 23:40; Nehemiah 8:15). They are thus associated with times of renewal through obedience to God's word.
3. In the intertestamental period, palms were used in the celebrations in connection with the resanctification of the temple by Simon Maccabee (1 Maccabees 13:37,51; 2 Maccabees 10:7). Thus the branches on Palm Sunday are a fitting prelude to the cleansing of the temple in Matthew 21, Mark 11, and Luke 19.
4. They also suggest victory (Revelation 7:9). And in Psalm 92:12 they are associated with growth and flourishing.