The Hebrew word for waiter is meltzar מלצר (feminine meltzarit מלצרית). But Klein has the following definition and etymology:
guardian [Probably from Akkadian massaru (=guardian).]
The Akkadian massaru is probably cognate with the Hebrew root נצר, also meaning "to guard" (which we discussed here).
How did meltzar get from guardian to waiter?
The word only appears twice in Biblical Hebrew, both in the first chapter of the Book of Daniel. The book begins with the king of Babylon calling for some Israelites (including Daniel) for training, to eventually enter the king's service.
The king allotted daily rations to them from the king’s food and from the wine he drank. They were to be educated for three years, at the end of which they were to enter the king’s service. (verse 5)
Daniel resolved not to defile himself with the king’s food or the wine he drank, so he sought permission of the chief officer not to defile himself, and God disposed the chief officer to be kind and compassionate toward Daniel. The chief officer said to Daniel, “I fear that my lord the king, who allotted food and drink to you, will notice that you look out of sorts, unlike the other youths of your age—and you will put my life in jeopardy with the king.” (verses 8-10)We here (verse 11) see the first appearance of the word meltzar:
וַיֹּ֥אמֶר דָּנִיֵּ֖אל אֶל־הַמֶּלְצַ֑ר אֲשֶׁ֤ר מִנָּה֙ שַׂ֣ר הַסָּֽרִיסִ֔ים עַל־דָּנִיֵּ֣אל חֲנַנְיָ֔ה מִֽישָׁאֵ֖ל וַעֲזַרְיָֽה׃
Daniel replied to the guard [meltzar] whom the chief officer had put in charge of Daniel, Hananiah, Mishael and AzariahAnd then we see the word once again in verse 16:
“Please test your servants for ten days, giving us legumes to eat and water to drink. Then compare our appearance with that of the youths who eat of the king’s food, and do with your servants as you see fit.” He agreed to this plan of theirs, and tested them for ten days. When the ten days were over, they looked better and healthier than all the youths who were eating of the king’s food. So the guard [meltzar] kept on removing their food, and the wine they were supposed to drink, and gave them legumes. (verses 12-16)
So since this guard was occupied with bringing and removing the food from Daniel and his friends, it's easy to understand how one might assume he was a waiter, not a guard. Rashi on verse 11 says that a meltzar is someone who organizes the portions of food and the dishes. He translates with a French word of which there are various versions. The scholar Moshe Katan says that Rashi most likely wrote מיישטר"א, which would make it a form of the Old French maistre - "master". That would make it related to the term maître d', which is an abbreviation of maître d'hôtel, meaning "the head of the house."
It is difficult to say if Rashi reflected this understanding of the word, or because of his influence made that the common meaning. Ben Yehuda defines the word as "steward", a person in charge of the affairs of the house, etc. This meaning contains both concepts presented in Rashi - someone who organizes the food (think of a steward or stewardess on an airplane), as well as master of the house.
However, as Elon Gilad writes here, Ben Yehuda did not want the word meltzar used for "waiter" in Modern Hebrew. He preferred dayal דייל (feminine dayelet דיילת). He coined dayal on the basis of the Talmudic Aramaic word dayala דיילא - "attendant", which in turn derives from the Greek word for slave or servant - doulos. Doulos is also the root of the English word doula, which literally means "female slave".
However, as happened on more than one occasion, Ben Yehuda's plans did not win out, and people continued referring to waiters as meltzarim. But his word dayal was eventually redeemed - when El Al airlines was founded in 1948, they needed a specialized word for someone attending to passengers - and so a few years later, dayal became the Hebrew word for steward. Quite the journey for these words!