John Lightfoot on Matthew 21:8

[Strewed branches in the way.] Not that they strewed garments and boughs just in the way under the feet of the ass to be trod on; this perhaps might have thrown down the rider; but by the wayside they made little tents and tabernacles of clothes and boughs, according to the custom of the feast of Tabernacles. John also adds, that taking branches of palm trees in their hands, they went forth to meet him. That book of Maimonides entitled Tabernacles and palm branches, will be an excellent comment on this place, and so will the Talmudic treatise, Succah. We will pick out these few things, not unsuitable to the present story: "Doth any one spread his garment on his tabernacle against the heat of the sun, &c.? it is absurd; but if he spread his garment for comeliness and ornament, it is approved." Again, "The boughs of palm trees, of which the law, Leviticus 23:40, speaks, are the young growing sprouts of palms, before their leaves shoot out on all sides; but when they are like small staves, and these are called young branches of palms." And a little after, "It is a notable precept, to gather young branches of palms, the boughs of myrtle and willow, and to make them up into a small bundle, and to carry them in their hands," &c.