First, let me review the setting.
Zechariah is a priest, and he’s fulfilling his Temple duty, as chosen by lot. Basically, they would draw straws, and each eligible priest would get to serve one of many duties in the Temple on a rotation (there being more priests than duties). This was held to be a great honor.
The Bible says he was serving during the “hour of incense” which refers to the time of the lighting of the incense in the holy place. If you look at a diagram of the Temple,
that was just outside the “MOST” holy place, which no one ever went into except the high priest (only one of those) and that once a year. So he’s in that outer room, and with the larger crowd being gathered outside when the incense is lit, it means likely a Sabbath day, and they’re all there for service. The priest goes in to light the incense on the Altar of Incense as a symbol of the prayers of God’s people.
So that’s the physical setting.
Zechariah’s in there and no one can see him because he’s in the Temple alone in front of the altar. The bread table is on the right of the altar, and the menorah (the seven branched lamp stand) is on the left.
Luke then says, Gabriel is revealed, between the altar and the bread table. Why there, on the right side of the Altar? Well, the text doesn’t say, but in Jewish thought the right side is always the side of favor; of blessing. Consider Matthew 25:33, when Jesus separates the human race on Judgment day. The blessed go on “his right”, the cursed, to the left.
This is just a carryover from the symbolism of the Psalms that talk about God’s mighty “right hand” (Ps 20:6; 89:13). In a world where most people are right handed, the right hand came to symbolize power. As most people favor their right hand, so the right became naturally associated with favor. (They were not politically correct enough to consider how this might offend “other handed” people!) Gabriel’s message is clearly one of blessing and favor not only for Zechariah but for all of Israel, so this fits.
Now, since the text doesn’t actually say why Gabriel showed up there, this is one of those little details in Scripture that gives it the ring of an eye witness account. I mean, truly, why exactly IS Gabriel mentioned as appearing on the right of the Altar? Luke doesn’t answer the question.
Well, it’s likely that this is simply how Zechariah remembers it happening; a little firsthand nugget of detail that Luke found as he researched the story carefully (Luke 1:1-4). It’s the same way with other weird details that are unexplained, like John 21:11 that mentions the exact number and size of fish caught (153/large) with no explanation why! The point of such detail may have some symbolic significance, but where one is not explicitly given, the most obvious impact of such details is to tell us: this really happened because real eye witness memories often contain seemingly minor details of things that hit us.