12:13a

They took palm branches and went out to meet Him: This took place on “the next day” mentioned in 12:12. The word They refers back to the great crowd also mentioned there. The people in the crowd cut branches off some of the palm trees that were growing there. Then they carried the branches in their hands to wave and celebrate Jesus’ coming. This was the custom at this time as a way to welcome a famous person. In some languages it may be natural to make some of this explicit. For example:

and went out to meet him with palm branches in their hands (Phillips’ New Testament in Modern English)
-or-
the people went out ⌊of the city⌋ to welcome him, ⌊waving⌋ palm branches

palm branches: This phrase refers to the parts of a palm plant/tree that grow out of the trunk. See the picture below where the man is cutting a “branch” off of the trunk of a palm tree. In many languages, these branches are referred to as “leaves,” and that is really what they are. Also, some languages do not call a palm a “tree” because they do not have wood branches like a regular tree. Other areas may not have any plants like palms. You should refer to these palms and their branches in ways that are natural in your language. For example:

palm leaves
-or-
leaves from a palm plant
-or-
leafy branches
-or-
leaves from a plant like a coconut