As Yeshua was passing through Jericho, there was a little guy who was a chief tax-gatherer who wanted to see Yeshua. And, as the story goes, he climbed a sycamore tree so he could see Him.
The multitudes heard of the miracles performed by Yeshua and were desiring to honor Him as Messiah. It would appear that the use of the branches might indicate that they are offering Him as a “wave offering” to Yahweh (Num. 8:11-13). Yeshua is presented as the Lamb of Elohim and is honored in a similar way after His return (Rev. 7:9-10).