Why indeed? An answer will help us understand the overall text of Revelation. This is a good thing to ask when reading the Bible.
We learn all we need to learn from Book of Revelation itself. We don't know the full background, but the answers we need are there.
Who are these 'elders'?
Let's review who these elders are, and the word "elder" itself.
They are first mentioned in 4:4...
Revelation 4:4 (boldface added)
Around the throne were twenty-four thrones; and upon the thrones I saw twenty-four elders sitting, clothed in white garments, and golden crowns on their heads.
καὶ κυκλόθεν τοῦ θρόνου θρόνοι εἴκοσι τέσσαρες, καὶ ἐπὶ τοὺς θρόνους εἴκοσι τέσσαρας πρεσβυτέρους καθημένους περιβεβλημένους ἐν ἱματίοις λευκοῖς, καὶ ἐπὶ τὰς κεφαλὰς αὐτῶν στεφάνους χρυσοῦς.
The word "elder" comes from the adjective πρεσβύτερος (presbuteros, Strong's 4245).
Usage: elder, usually used as subst.; an elder, a member of the Sanhedrin, an elder of a Christian assembly.
We don't have any further definition of their function from the passage about what this word "elder" would have meant. The strongest thing we learn is that, being used to describe a member of the Sanhedrin, they were likely a governing body. The Sanhedrin did have legislative and legal powers, which was why Pontius Pilate would have had trouble dealing the Jewish leaders as they were a semi- or at least quasi-legal force to be reckoned with.
From 4:4, we also learn that they sit on thrones that are around "The Throne", they are clothed in white, and they wear crowns. These words mean basically the same thing in English and Greek, but here are some references for deeper study...
"throne" - θρόνος (thronos, 2362)
"white" - λευκός (leukos, 3022) or "bright"
"crown" - στέφανος (stephanos, 4735) or "wreath" or other honorary adornment for the head
Except the insight that "elder" was also used for voting members of the Sanhedrin, the Greek words basically mean the same thing in English.
This almost looks like a version of the Roman Senate, but instead of being seated in arrangement around Caesar or a speaker's podium, they are seated around God Himself on His Throne, and they are referred to by names reserved for religious-government legislative bodies, not purely government legislative bodies. So, they are both government and led by God Himself.
In 4:10, they cast down their crowns, verifying that they are seated under the authority of God on the Throne.
Revelation 4:10 (NASB) (emphasis added)
the twenty-four elders will fall down before Him who sits on the throne, and will worship Him who lives forever and ever, and will cast their crowns before the throne, saying,
What is this 'incense'?
Incense appears elsewhere in Revelation...
The "incense" from 5:8 is from θυμίαμα (thumiama, Strong's 2368), which also has a reference to "burning" or "fragrant stuff for burning, incense" (Vine's). Again, the English meaning is basically the same as the Greek.
From 5:8, we do know that this incense is the "prayers of the saints".
Incense also appears in Chapter 8...
Revelation 8:3-5 (NASB)
3 Another angel came and stood at the altar, holding a golden censer; and much incense was given to him, so that he might add it to the prayers of all the saints on the golden altar which was before the throne. 4 And the smoke of the incense, with the prayers of the saints, went up before God out of the angel’s hand. 5 Then the angel took the censer and filled it with the fire of the altar, and threw it to the earth; and there followed peals of thunder and sounds and flashes of lightning and an earthquake.
In v3, we learn that incense on the golden altar was the prayers of all the saints—Greek trying to explain that all prayer/incense goes to the altar. In v4, the prayers rise up before the Lord in the form of incense. In v6, we see that these prayers make quite a big difference on earth.
Moreover, looking back at v3, we see that the business of the throne room in Heaven was interrupted for this matter of incense and prayers from the saints to do important work on earth. The three verses in 8:3-5 are an interruption of the events that began in ch4.
So, we can conclude that prayer/incense is important around the throne of God and is important enough to interrupt other business in the throne room.
We could even argue that, since each elder has a bowl dedicated to this prayer/incense, and that the altar before the throne itself is the final destination of all this prayer/incense, that prayer itself is one of the primary functions of the throne room—and delivering or handling collected prayers requests before the the Lord is a primary function of these elders. They also have harps, and there is worship in the throne room, so prayer is not the only function of the throne room, but one of the most important functions.
This is consistent with how many kings and even government leaders operate today, who take time to hear out the petitions and requests of the people, in any form of government.
What is the altar for?
The altar seems to be a central collection place for prayer/incense. We learn more about what happens there in ch6 when the fifth seal is opened.
Revelation 6:9-11 (NASB)
9 When the Lamb broke the fifth seal, I saw underneath the altar the souls of those who had been slain because of the word of God, and because of the testimony which they had maintained; 10 and they cried out with a loud voice, saying, “How long, O Lord, holy and true, will You refrain from judging and avenging our blood on those who dwell on the earth?” 11 And there was given to each of them a white robe; and they were told that they should rest for a little while longer, until the number of their fellow servants and their brethren who were to be killed even as they had been, would be completed also.
Apparently, Christian martyrs are under the altar, making their own prayer/incense petition to God directly. They aren't making petitions through a legislative body like a Senate or Sanhedrin, but directly. This is a contrast.
These elders are public servants hearing out the needs of the people as the servant leaders Jesus described. Being leaders under God and the Lamb, these leaders must have met Jesus's qualifications for leadership...
Matthew 20:26 (NASB)
It is not this way among you, but whoever wishes to become great among you shall be your servant,
So, what is the bowl in the hands of an elder for? To deliver the requests of the people through God's government administration.